algebra.algebra.operations ⟷ Mathlib.Algebra.Algebra.Operations

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

@@ -483,7 +483,7 @@ variable (M)
 #print Submodule.span_pow /-
 theorem span_pow (s : Set A) : ∀ n : ℕ, span R s ^ n = span R (s ^ n)
   | 0 => by rw [pow_zero, pow_zero, one_eq_span_one_set]
-  | n + 1 => by rw [pow_succ, pow_succ, span_pow, span_mul_span]
+  | n + 1 => by rw [pow_succ', pow_succ', span_pow, span_mul_span]
 #align submodule.span_pow Submodule.span_pow
 -/
 
@@ -510,7 +510,7 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
   by
   induction' n with n ih
   · exact (h rfl).elim
-  · rw [pow_succ, pow_succ, mul_to_add_submonoid]
+  · rw [pow_succ', pow_succ', mul_to_add_submonoid]
     cases n
     · rw [pow_zero, pow_zero, mul_one, ← mul_to_add_submonoid, mul_one]
     · rw [ih n.succ_ne_zero]
@@ -551,8 +551,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
     (hr : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
     (hadd : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
-    (hmul :
-      ∀ i x hx, C i x hx → ∀ m ∈ M, C i.succ (x * m) ((pow_succ' M i).symm ▸ mul_mem_mul hx H))
+    (hmul : ∀ i x hx, C i x hx → ∀ m ∈ M, C i.succ (x * m) ((pow_succ M i).symm ▸ mul_mem_mul hx H))
     {x : A} {n : ℕ} (hx : x ∈ M ^ n) : C n x hx :=
   by
   induction' n with n n_ih generalizing x
@@ -560,7 +559,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   revert hx
-  simp_rw [pow_succ']
+  simp_rw [pow_succ]
   intro hx
   exact
     Submodule.mul_induction_on' (fun m hm x ih => hmul _ _ hm (n_ih _) _ ih)

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

@@ -214,7 +214,7 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
     (hm : ∀ m ∈ M, ∀ n ∈ N, C (m * n)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
   by
-  rw [← mem_to_add_submonoid, mul_to_add_submonoid] at hr 
+  rw [← mem_to_add_submonoid, mul_to_add_submonoid] at hr
   exact AddSubmonoid.mul_induction_on hr hm ha
 #align submodule.mul_induction_on Submodule.mul_induction_on
 -/
@@ -332,7 +332,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
       · obtain ⟨y', hy', fy_eq⟩ := mem_map.mp y.2
         use y', hy'
         refine' trans _ hy
-        rw [f.to_linear_map_apply] at fy_eq 
+        rw [f.to_linear_map_apply] at fy_eq
         ext
         simp [fy_eq]
 #align submodule.map_mul Submodule.map_mul
@@ -446,7 +446,7 @@ theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
   Submodule.mem_span_mul_finite_of_mem_span_mul
-    (by rwa [← Submodule.span_eq P, ← Submodule.span_eq Q, Submodule.span_mul_span] at hx )
+    (by rwa [← Submodule.span_eq P, ← Submodule.span_eq Q, Submodule.span_mul_span] at hx)
 #align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mul
 -/
 
@@ -536,7 +536,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
     (hx : x ∈ M ^ n) : C n x hx :=
   by
   induction' n with n n_ih generalizing x
-  · rw [pow_zero] at hx 
+  · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   exact
@@ -556,7 +556,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     {x : A} {n : ℕ} (hx : x ∈ M ^ n) : C n x hx :=
   by
   induction' n with n n_ih generalizing x
-  · rw [pow_zero] at hx 
+  · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   revert hx
@@ -835,7 +835,7 @@ theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   by
   constructor; all_goals intro hI
-  · rwa [le_div_iff_mul_le, one_mul] at hI 
+  · rwa [le_div_iff_mul_le, one_mul] at hI
   · rwa [le_div_iff_mul_le, one_mul]
 #align submodule.one_le_one_div Submodule.one_le_one_div
 -/
@@ -854,7 +854,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
   intro m hm n hn
-  rw [Submodule.mem_div_iff_forall_mul_mem] at hn 
+  rw [Submodule.mem_div_iff_forall_mul_mem] at hn
   rw [mul_comm]
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one

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

@@ -770,8 +770,8 @@ theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A} (h₁ : s.down
 #align submodule.smul_le_smul Submodule.smul_le_smul
 -/
 
-#print Submodule.smul_singleton /-
-theorem smul_singleton (a : A) (M : Submodule R A) :
+#print Submodule.singleton_smul /-
+theorem singleton_smul (a : A) (M : Submodule R A) :
     ({a} : Set A).up • M = M.map (LinearMap.mulLeft R a) :=
   by
   conv_lhs => rw [← span_eq M]
@@ -783,7 +783,7 @@ theorem smul_singleton (a : A) (M : Submodule R A) :
     rw [SetLike.mem_coe, mem_map, set.mem_singleton_iff.mp hb]
     exact ⟨m, hm, rfl⟩
   · rintro _ ⟨m, hm, rfl⟩; exact subset_span ⟨a, m, Set.mem_singleton a, hm, rfl⟩
-#align submodule.smul_singleton Submodule.smul_singleton
+#align submodule.smul_singleton Submodule.singleton_smul
 -/
 
 section Quotient

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

@@ -3,16 +3,16 @@ Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 -/
-import Mathbin.Algebra.Algebra.Bilinear
-import Mathbin.Algebra.Algebra.Equiv
-import Mathbin.Algebra.Module.Submodule.Pointwise
-import Mathbin.Algebra.Module.Submodule.Bilinear
-import Mathbin.Algebra.Module.Opposites
-import Mathbin.Algebra.Order.Kleene
-import Mathbin.Data.Finset.Pointwise
-import Mathbin.Data.Set.Semiring
-import Mathbin.Data.Set.Pointwise.BigOperators
-import Mathbin.GroupTheory.GroupAction.SubMulAction.Pointwise
+import Algebra.Algebra.Bilinear
+import Algebra.Algebra.Equiv
+import Algebra.Module.Submodule.Pointwise
+import Algebra.Module.Submodule.Bilinear
+import Algebra.Module.Opposites
+import Algebra.Order.Kleene
+import Data.Finset.Pointwise
+import Data.Set.Semiring
+import Data.Set.Pointwise.BigOperators
+import GroupTheory.GroupAction.SubMulAction.Pointwise
 
 #align_import algebra.algebra.operations from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -840,7 +840,7 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
 #align submodule.one_le_one_div Submodule.one_le_one_div
 -/
 
-/- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
+/- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:133:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
 #print Submodule.le_self_mul_one_div /-
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -684,7 +684,7 @@ This is a stronger version of `submodule.pointwise_distrib_mul_action`. -/
 protected def pointwiseMulSemiringAction : MulSemiringAction α (Submodule R A) :=
   {
     Submodule.pointwiseDistribMulAction with
-    smul_mul := fun r x y => Submodule.map_mul x y <| MulSemiringAction.toAlgHom R A r
+    smul_hMul := fun r x y => Submodule.map_mul x y <| MulSemiringAction.toAlgHom R A r
     smul_one := fun r => Submodule.map_one <| MulSemiringAction.toAlgHom R A r }
 #align submodule.pointwise_mul_semiring_action Submodule.pointwiseMulSemiringAction
 -/
@@ -748,7 +748,7 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A)
   smul s P := span R s.down * P
   smul_add _ _ _ := mul_add _ _ _
   add_smul s t P := by simp_rw [SMul.smul, SetSemiring.down_add, span_union, sup_mul, add_eq_sup]
-  mul_smul s t P := by simp_rw [SMul.smul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
+  hMul_smul s t P := by simp_rw [SMul.smul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
   one_smul P := by simp_rw [SMul.smul, SetSemiring.down_one, ← one_eq_span_one_set, one_mul]
   zero_smul P := by simp_rw [SMul.smul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
   smul_zero _ := mul_bot _

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module algebra.algebra.operations
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Bilinear
 import Mathbin.Algebra.Algebra.Equiv
@@ -19,6 +14,8 @@ import Mathbin.Data.Set.Semiring
 import Mathbin.Data.Set.Pointwise.BigOperators
 import Mathbin.GroupTheory.GroupAction.SubMulAction.Pointwise
 
+#align_import algebra.algebra.operations from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Multiplication and division of submodules of an algebra.
 

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

@@ -60,13 +60,17 @@ namespace SubMulAction
 
 variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 
+#print SubMulAction.algebraMap_mem /-
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
 #align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_mem
+-/
 
+#print SubMulAction.mem_one' /-
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
 #align sub_mul_action.mem_one' SubMulAction.mem_one'
+-/
 
 end SubMulAction
 
@@ -92,20 +96,26 @@ theorem one_eq_range : (1 : Submodule R A) = (Algebra.linearMap R A).range :=
 #align submodule.one_eq_range Submodule.one_eq_range
 -/
 
+#print Submodule.le_one_toAddSubmonoid /-
 theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
   by
   rintro x ⟨n, rfl⟩
   exact ⟨n, map_natCast (algebraMap R A) n⟩
 #align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoid
+-/
 
+#print Submodule.algebraMap_mem /-
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
 #align submodule.algebra_map_mem Submodule.algebraMap_mem
+-/
 
+#print Submodule.mem_one /-
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
   Iff.rfl
 #align submodule.mem_one Submodule.mem_one
+-/
 
 #print Submodule.toSubMulAction_one /-
 @[simp]
@@ -135,47 +145,62 @@ theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
 #align submodule.one_le Submodule.one_le
 -/
 
+#print Submodule.map_one /-
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (1 : Submodule R A) = 1 := by ext; simp
 #align submodule.map_one Submodule.map_one
+-/
 
+#print Submodule.map_op_one /-
 @[simp]
 theorem map_op_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 := by ext;
   induction x using MulOpposite.rec'; simp
 #align submodule.map_op_one Submodule.map_op_one
+-/
 
+#print Submodule.comap_op_one /-
 @[simp]
 theorem comap_op_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 := by ext;
   simp
 #align submodule.comap_op_one Submodule.comap_op_one
+-/
 
+#print Submodule.map_unop_one /-
 @[simp]
 theorem map_unop_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R Aᵐᵒᵖ) = 1 := by
   rw [← comap_equiv_eq_map_symm, comap_op_one]
 #align submodule.map_unop_one Submodule.map_unop_one
+-/
 
+#print Submodule.comap_unop_one /-
 @[simp]
 theorem comap_unop_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R A) = 1 := by
   rw [← map_equiv_eq_comap_symm, map_op_one]
 #align submodule.comap_unop_one Submodule.comap_unop_one
+-/
 
 /-- Multiplication of sub-R-modules of an R-algebra A. The submodule `M * N` is the
 smallest R-submodule of `A` containing the elements `m * n` for `m ∈ M` and `n ∈ N`. -/
 instance : Mul (Submodule R A) :=
   ⟨Submodule.map₂ <| LinearMap.mul R A⟩
 
+#print Submodule.mul_mem_mul /-
 theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
   apply_mem_map₂ _ hm hn
 #align submodule.mul_mem_mul Submodule.mul_mem_mul
+-/
 
+#print Submodule.mul_le /-
 theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
   map₂_le
 #align submodule.mul_le Submodule.mul_le
+-/
 
+#print Submodule.mul_toAddSubmonoid /-
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid :=
   by
@@ -185,7 +210,9 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
   rw [supr_to_add_submonoid]
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
+-/
 
+#print Submodule.mul_induction_on /-
 @[elab_as_elim]
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
     (hm : ∀ m ∈ M, ∀ n ∈ N, C (m * n)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -193,7 +220,9 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
   rw [← mem_to_add_submonoid, mul_to_add_submonoid] at hr 
   exact AddSubmonoid.mul_induction_on hr hm ha
 #align submodule.mul_induction_on Submodule.mul_induction_on
+-/
 
+#print Submodule.mul_induction_on' /-
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
 protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
@@ -205,12 +234,15 @@ protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
     Submodule.mul_induction_on hr (fun x hx y hy => ⟨_, hm _ hx _ hy⟩) fun x y ⟨_, hx⟩ ⟨_, hy⟩ =>
       ⟨_, ha _ _ _ _ hx hy⟩
 #align submodule.mul_induction_on' Submodule.mul_induction_on'
+-/
 
 variable (R)
 
+#print Submodule.span_mul_span /-
 theorem span_mul_span : span R S * span R T = span R (S * T) :=
   map₂_span_span _ _ _ _
 #align submodule.span_mul_span Submodule.span_mul_span
+-/
 
 variable {R}
 
@@ -223,10 +255,12 @@ theorem mul_bot : M * ⊥ = ⊥ :=
 #align submodule.mul_bot Submodule.mul_bot
 -/
 
+#print Submodule.bot_mul /-
 @[simp]
 theorem bot_mul : ⊥ * M = ⊥ :=
   map₂_bot_left _ _
 #align submodule.bot_mul Submodule.bot_mul
+-/
 
 #print Submodule.one_mul /-
 @[simp]
@@ -271,14 +305,19 @@ theorem mul_sup : M * (N ⊔ P) = M * N ⊔ M * P :=
 #align submodule.mul_sup Submodule.mul_sup
 -/
 
+#print Submodule.sup_mul /-
 theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
   map₂_sup_left _ _ _ _
 #align submodule.sup_mul Submodule.sup_mul
+-/
 
+#print Submodule.mul_subset_mul /-
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
   image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
+-/
 
+#print Submodule.map_mul /-
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
   calc
@@ -300,7 +339,9 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
         ext
         simp [fy_eq]
 #align submodule.map_mul Submodule.map_mul
+-/
 
+#print Submodule.map_op_mul /-
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
@@ -316,14 +357,18 @@ theorem map_op_mul :
     rw [Submodule.mem_map_equiv] at hm hn ⊢
     exact mul_mem_mul hn hm
 #align submodule.map_op_mul Submodule.map_op_mul
+-/
 
+#print Submodule.comap_unop_mul /-
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
         comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M :=
   by simp_rw [← map_equiv_eq_comap_symm, map_op_mul]
 #align submodule.comap_unop_mul Submodule.comap_unop_mul
+-/
 
+#print Submodule.map_unop_mul /-
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
@@ -334,13 +379,16 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     rw [← map_comp, map_op_mul, ← map_comp, ← map_comp, LinearEquiv.comp_coe,
       LinearEquiv.symm_trans_self, LinearEquiv.refl_toLinearMap, map_id, map_id, map_id]
 #align submodule.map_unop_mul Submodule.map_unop_mul
+-/
 
+#print Submodule.comap_op_mul /-
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
         comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M :=
   by simp_rw [comap_equiv_eq_map_symm, map_unop_mul]
 #align submodule.comap_op_mul Submodule.comap_op_mul
+-/
 
 section
 
@@ -363,6 +411,7 @@ section DecidableEq
 
 open scoped Classical
 
+#print Submodule.mem_span_mul_finite_of_mem_span_mul /-
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :
     ∃ T T' : Finset A, ↑T ⊆ S ∧ ↑T' ⊆ S' ∧ x ∈ span R (T * T' : Set A) :=
@@ -374,16 +423,21 @@ theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A]
   have h'' := span_mono h' hU
   assumption
 #align submodule.mem_span_mul_finite_of_mem_span_mul Submodule.mem_span_mul_finite_of_mem_span_mul
+-/
 
 end DecidableEq
 
+#print Submodule.mul_eq_span_mul_set /-
 theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A) * (t : Set A)) :=
   map₂_eq_span_image2 _ s t
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
+-/
 
+#print Submodule.iSup_mul /-
 theorem iSup_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
   map₂_iSup_left _ s t
 #align submodule.supr_mul Submodule.iSup_mul
+-/
 
 #print Submodule.mul_iSup /-
 theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
@@ -391,21 +445,27 @@ theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s
 #align submodule.mul_supr Submodule.mul_iSup
 -/
 
+#print Submodule.mem_span_mul_finite_of_mem_mul /-
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
   Submodule.mem_span_mul_finite_of_mem_span_mul
     (by rwa [← Submodule.span_eq P, ← Submodule.span_eq Q, Submodule.span_mul_span] at hx )
 #align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mul
+-/
 
 variable {M N P}
 
+#print Submodule.mem_span_singleton_mul /-
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x := by
   simp_rw [(· * ·), map₂_span_singleton_eq_map, exists_prop]; rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
+-/
 
+#print Submodule.mem_mul_span_singleton /-
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x := by
   simp_rw [(· * ·), map₂_span_singleton_eq_map_flip, exists_prop]; rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
+-/
 
 /-- Sub-R-modules of an R-algebra form an idempotent semiring. -/
 instance : IdemSemiring (Submodule R A) :=
@@ -436,9 +496,11 @@ theorem pow_eq_span_pow_set (n : ℕ) : M ^ n = span R ((M : Set A) ^ n) := by
 #align submodule.pow_eq_span_pow_set Submodule.pow_eq_span_pow_set
 -/
 
+#print Submodule.pow_subset_pow /-
 theorem pow_subset_pow {n : ℕ} : (↑M : Set A) ^ n ⊆ ↑(M ^ n : Submodule R A) :=
   (pow_eq_span_pow_set M n).symm ▸ subset_span
 #align submodule.pow_subset_pow Submodule.pow_subset_pow
+-/
 
 #print Submodule.pow_mem_pow /-
 theorem pow_mem_pow {x : A} (hx : x ∈ M) (n : ℕ) : x ^ n ∈ M ^ n :=
@@ -458,13 +520,16 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
 #align submodule.pow_to_add_submonoid Submodule.pow_toAddSubmonoid
 -/
 
+#print Submodule.le_pow_toAddSubmonoid /-
 theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAddSubmonoid :=
   by
   obtain rfl | hn := Decidable.eq_or_ne n 0
   · rw [pow_zero, pow_zero]; exact le_one_to_add_submonoid
   · exact (pow_to_add_submonoid M hn).ge
 #align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoid
+-/
 
+#print Submodule.pow_induction_on_left' /-
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -481,7 +546,9 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
     Submodule.mul_induction_on' (fun m hm x ih => hmul _ hm _ _ _ (n_ih ih))
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'
+-/
 
+#print Submodule.pow_induction_on_right' /-
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -502,7 +569,9 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     Submodule.mul_induction_on' (fun m hm x ih => hmul _ _ hm (n_ih _) _ ih)
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'
+-/
 
+#print Submodule.pow_induction_on_left /-
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -512,7 +581,9 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
   Submodule.pow_induction_on_left' M hr (fun x y i hx hy => hadd x y)
     (fun m hm i x hx => hmul _ hm _) hx
 #align submodule.pow_induction_on_left Submodule.pow_induction_on_left
+-/
 
+#print Submodule.pow_induction_on_right /-
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -521,6 +592,7 @@ protected theorem pow_induction_on_right {C : A → Prop} (hr : ∀ r : R, C (al
     (hx : x ∈ M ^ n) : C x :=
   Submodule.pow_induction_on_right' M hr (fun x y i hx hy => hadd x y) (fun i x hx => hmul _) hx
 #align submodule.pow_induction_on_right Submodule.pow_induction_on_right
+-/
 
 #print Submodule.mapHom /-
 /-- `submonoid.map` as a `monoid_with_zero_hom`, when applied to `alg_hom`s. -/
@@ -534,6 +606,7 @@ def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R
 #align submodule.map_hom Submodule.mapHom
 -/
 
+#print Submodule.equivOpposite /-
 /-- The ring of submodules of the opposite algebra is isomorphic to the opposite ring of
 submodules. -/
 @[simps apply symm_apply]
@@ -546,36 +619,48 @@ def equivOpposite : Submodule R Aᵐᵒᵖ ≃+* (Submodule R A)ᵐᵒᵖ
   map_add' p q := by simp [comap_equiv_eq_map_symm, ← op_add]
   map_mul' p q := congr_arg op <| comap_op_mul _ _
 #align submodule.equiv_opposite Submodule.equivOpposite
+-/
 
+#print Submodule.map_pow /-
 protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') (n : ℕ) :
     map f.toLinearMap (M ^ n) = map f.toLinearMap M ^ n :=
   map_pow (mapHom f) M n
 #align submodule.map_pow Submodule.map_pow
+-/
 
+#print Submodule.comap_unop_pow /-
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).symm.map_pow (op M) n
 #align submodule.comap_unop_pow Submodule.comap_unop_pow
+-/
 
+#print Submodule.comap_op_pow /-
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   op_injective <| (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).map_pow M n
 #align submodule.comap_op_pow Submodule.comap_op_pow
+-/
 
+#print Submodule.map_op_pow /-
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   by rw [map_equiv_eq_comap_symm, map_equiv_eq_comap_symm, comap_unop_pow]
 #align submodule.map_op_pow Submodule.map_op_pow
+-/
 
+#print Submodule.map_unop_pow /-
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   by rw [← comap_equiv_eq_map_symm, ← comap_equiv_eq_map_symm, comap_op_pow]
 #align submodule.map_unop_pow Submodule.map_unop_pow
+-/
 
+#print Submodule.span.ringHom /-
 /-- `span` is a semiring homomorphism (recall multiplication is pointwise multiplication of subsets
 on either side). -/
 @[simps]
@@ -587,11 +672,13 @@ def span.ringHom : SetSemiring A →+* Submodule R A
   map_add' := span_union
   map_mul' s t := by rw [SetSemiring.down_mul, span_mul_span, ← image_mul_prod]
 #align submodule.span.ring_hom Submodule.span.ringHom
+-/
 
 section
 
 variable {α : Type _} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A]
 
+#print Submodule.pointwiseMulSemiringAction /-
 /-- The action on a submodule corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale.
@@ -603,6 +690,7 @@ protected def pointwiseMulSemiringAction : MulSemiringAction α (Submodule R A)
     smul_mul := fun r x y => Submodule.map_mul x y <| MulSemiringAction.toAlgHom R A r
     smul_one := fun r => Submodule.map_one <| MulSemiringAction.toAlgHom R A r }
 #align submodule.pointwise_mul_semiring_action Submodule.pointwiseMulSemiringAction
+-/
 
 scoped[Pointwise] attribute [instance] Submodule.pointwiseMulSemiringAction
 
@@ -616,9 +704,11 @@ variable {A : Type v} [CommSemiring A] [Algebra R A]
 
 variable {M N : Submodule R A} {m n : A}
 
+#print Submodule.mul_mem_mul_rev /-
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=
   mul_comm m n ▸ mul_mem_mul hm hn
 #align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_rev
+-/
 
 variable (M N)
 
@@ -633,6 +723,7 @@ protected theorem mul_comm : M * N = N * M :=
 instance : IdemCommSemiring (Submodule R A) :=
   { Submodule.idemSemiring with mul_comm := Submodule.mul_comm }
 
+#print Submodule.prod_span /-
 theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     ∏ i in s, Submodule.span R (M i) = Submodule.span R (∏ i in s, M i) :=
   by
@@ -642,14 +733,18 @@ theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
   · intro _ _ H ih
     rw [Finset.prod_insert H, Finset.prod_insert H, ih, span_mul_span]
 #align submodule.prod_span Submodule.prod_span
+-/
 
+#print Submodule.prod_span_singleton /-
 theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
     ∏ i in s, span R ({x i} : Set A) = span R {∏ i in s, x i} := by
   rw [prod_span, Set.finset_prod_singleton]
 #align submodule.prod_span_singleton Submodule.prod_span_singleton
+-/
 
 variable (R A)
 
+#print Submodule.moduleSet /-
 /-- R-submodules of the R-algebra A are a module over `set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A)
     where
@@ -661,6 +756,7 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A)
   zero_smul P := by simp_rw [SMul.smul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
   smul_zero _ := mul_bot _
 #align submodule.module_set Submodule.moduleSet
+-/
 
 variable {R A}
 
@@ -712,23 +808,32 @@ instance : Div (Submodule R A) :=
         rw [Algebra.smul_mul_assoc]
         exact Submodule.smul_mem _ _ (hx _ hy) }⟩
 
+#print Submodule.mem_div_iff_forall_mul_mem /-
 theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I :=
   Iff.refl _
 #align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_mem
+-/
 
+#print Submodule.mem_div_iff_smul_subset /-
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
   ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by rw [← xy'_eq_y]; apply h; assumption, fun h y hy =>
     h (Set.smul_mem_smul_set hy)⟩
 #align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subset
+-/
 
+#print Submodule.le_div_iff /-
 theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z ∈ K, x * z ∈ J :=
   Iff.refl _
 #align submodule.le_div_iff Submodule.le_div_iff
+-/
 
+#print Submodule.le_div_iff_mul_le /-
 theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J := by
   rw [le_div_iff, mul_le]
 #align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_le
+-/
 
+#print Submodule.one_le_one_div /-
 @[simp]
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   by
@@ -736,6 +841,7 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   · rwa [le_div_iff_mul_le, one_mul] at hI 
   · rwa [le_div_iff_mul_le, one_mul]
 #align submodule.one_le_one_div Submodule.one_le_one_div
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
 #print Submodule.le_self_mul_one_div /-
@@ -757,6 +863,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
 -/
 
+#print Submodule.map_div /-
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)
     (h : A ≃ₐ[R] B) : (I / J).map h.toLinearMap = I.map h.toLinearMap / J.map h.toLinearMap :=
@@ -773,6 +880,7 @@ protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Sub
     apply h.injective
     erw [h.map_mul, h.apply_symm_apply, hxz]
 #align submodule.map_div Submodule.map_div
+-/
 
 end Quotient
 

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

@@ -634,7 +634,7 @@ instance : IdemCommSemiring (Submodule R A) :=
   { Submodule.idemSemiring with mul_comm := Submodule.mul_comm }
 
 theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
-    (∏ i in s, Submodule.span R (M i)) = Submodule.span R (∏ i in s, M i) :=
+    ∏ i in s, Submodule.span R (M i) = Submodule.span R (∏ i in s, M i) :=
   by
   letI := Classical.decEq ι
   refine' Finset.induction_on s _ _
@@ -644,7 +644,7 @@ theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
 #align submodule.prod_span Submodule.prod_span
 
 theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
-    (∏ i in s, span R ({x i} : Set A)) = span R {∏ i in s, x i} := by
+    ∏ i in s, span R ({x i} : Set A) = span R {∏ i in s, x i} := by
   rw [prod_span, Set.finset_prod_singleton]
 #align submodule.prod_span_singleton Submodule.prod_span_singleton
 

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

@@ -299,7 +299,6 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
         rw [f.to_linear_map_apply] at fy_eq 
         ext
         simp [fy_eq]
-    
 #align submodule.map_mul Submodule.map_mul
 
 theorem map_op_mul :

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

@@ -705,7 +705,7 @@ This is the general form of the ideal quotient, traditionally written $I : J$.
 -/
 instance : Div (Submodule R A) :=
   ⟨fun I J =>
-    { carrier := { x | ∀ y ∈ J, x * y ∈ I }
+    { carrier := {x | ∀ y ∈ J, x * y ∈ I}
       zero_mem' := fun y hy => by rw [MulZeroClass.zero_mul]; apply Submodule.zero_mem
       add_mem' := fun a b ha hb y hy => by rw [add_mul];
         exact Submodule.add_mem _ (ha _ hy) (hb _ hy)

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

@@ -190,7 +190,7 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
     (hm : ∀ m ∈ M, ∀ n ∈ N, C (m * n)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
   by
-  rw [← mem_to_add_submonoid, mul_to_add_submonoid] at hr
+  rw [← mem_to_add_submonoid, mul_to_add_submonoid] at hr 
   exact AddSubmonoid.mul_induction_on hr hm ha
 #align submodule.mul_induction_on Submodule.mul_induction_on
 
@@ -296,7 +296,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
       · obtain ⟨y', hy', fy_eq⟩ := mem_map.mp y.2
         use y', hy'
         refine' trans _ hy
-        rw [f.to_linear_map_apply] at fy_eq
+        rw [f.to_linear_map_apply] at fy_eq 
         ext
         simp [fy_eq]
     
@@ -314,7 +314,7 @@ theorem map_op_mul :
     show op n * op m ∈ _
     exact mul_mem_mul hn hm
   · refine' mul_le.2 (MulOpposite.rec' fun m hm => MulOpposite.rec' fun n hn => _)
-    rw [Submodule.mem_map_equiv] at hm hn⊢
+    rw [Submodule.mem_map_equiv] at hm hn ⊢
     exact mul_mem_mul hn hm
 #align submodule.map_op_mul Submodule.map_op_mul
 
@@ -395,7 +395,7 @@ theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
   Submodule.mem_span_mul_finite_of_mem_span_mul
-    (by rwa [← Submodule.span_eq P, ← Submodule.span_eq Q, Submodule.span_mul_span] at hx)
+    (by rwa [← Submodule.span_eq P, ← Submodule.span_eq Q, Submodule.span_mul_span] at hx )
 #align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mul
 
 variable {M N P}
@@ -475,7 +475,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
     (hx : x ∈ M ^ n) : C n x hx :=
   by
   induction' n with n n_ih generalizing x
-  · rw [pow_zero] at hx
+  · rw [pow_zero] at hx 
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   exact
@@ -493,7 +493,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     {x : A} {n : ℕ} (hx : x ∈ M ^ n) : C n x hx :=
   by
   induction' n with n n_ih generalizing x
-  · rw [pow_zero] at hx
+  · rw [pow_zero] at hx 
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   revert hx
@@ -734,7 +734,7 @@ theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   by
   constructor; all_goals intro hI
-  · rwa [le_div_iff_mul_le, one_mul] at hI
+  · rwa [le_div_iff_mul_le, one_mul] at hI 
   · rwa [le_div_iff_mul_le, one_mul]
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
@@ -752,7 +752,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
   intro m hm n hn
-  rw [Submodule.mem_div_iff_forall_mul_mem] at hn
+  rw [Submodule.mem_div_iff_forall_mul_mem] at hn 
   rw [mul_comm]
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one

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

@@ -52,9 +52,9 @@ universe uι u v
 
 open Algebra Set MulOpposite
 
-open BigOperators
+open scoped BigOperators
 
-open Pointwise
+open scoped Pointwise
 
 namespace SubMulAction
 
@@ -129,9 +129,11 @@ theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
 -/
 
+#print Submodule.one_le /-
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
   simpa only [one_eq_span, span_le, Set.singleton_subset_iff]
 #align submodule.one_le Submodule.one_le
+-/
 
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (1 : Submodule R A) = 1 := by ext; simp
@@ -242,18 +244,24 @@ protected theorem mul_one : M * 1 = M := by conv_lhs => rw [one_eq_span, ← spa
 
 variable {M N P Q}
 
+#print Submodule.mul_le_mul /-
 @[mono]
 theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
   map₂_le_map₂ hmp hnq
 #align submodule.mul_le_mul Submodule.mul_le_mul
+-/
 
+#print Submodule.mul_le_mul_left /-
 theorem mul_le_mul_left (h : M ≤ N) : M * P ≤ N * P :=
   map₂_le_map₂_left h
 #align submodule.mul_le_mul_left Submodule.mul_le_mul_left
+-/
 
+#print Submodule.mul_le_mul_right /-
 theorem mul_le_mul_right (h : N ≤ P) : M * N ≤ M * P :=
   map₂_le_map₂_right h
 #align submodule.mul_le_mul_right Submodule.mul_le_mul_right
+-/
 
 variable (M N P)
 
@@ -337,7 +345,7 @@ theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
 
 section
 
-open Pointwise
+open scoped Pointwise
 
 #print Submodule.hasDistribPointwiseNeg /-
 /-- `submodule.has_pointwise_neg` distributes over multiplication.
@@ -354,7 +362,7 @@ end
 
 section DecidableEq
 
-open Classical
+open scoped Classical
 
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :
@@ -731,12 +739,15 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
+#print Submodule.le_self_mul_one_div /-
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
   by
   rw [← mul_one I]
   apply mul_le_mul_right (one_le_one_div.mpr hI)
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
+-/
 
+#print Submodule.mul_one_div_le_one /-
 theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
@@ -745,6 +756,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   rw [mul_comm]
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
+-/
 
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)

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

@@ -60,16 +60,10 @@ namespace SubMulAction
 
 variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 
-/- warning: sub_mul_action.algebra_map_mem -> SubMulAction.algebraMap_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
 #align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_mem
 
-/- warning: sub_mul_action.mem_one' -> SubMulAction.mem_one' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
 #align sub_mul_action.mem_one' SubMulAction.mem_one'
@@ -98,34 +92,16 @@ theorem one_eq_range : (1 : Submodule R A) = (Algebra.linearMap R A).range :=
 #align submodule.one_eq_range Submodule.one_eq_range
 -/
 
-/- warning: submodule.le_one_to_add_submonoid -> Submodule.le_one_toAddSubmonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toHasLe.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (OfNat.mk.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.one.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.toOfNat1.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.one.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
-Case conversion may be inaccurate. Consider using '#align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoidₓ'. -/
 theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
   by
   rintro x ⟨n, rfl⟩
   exact ⟨n, map_natCast (algebraMap R A) n⟩
 #align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoid
 
-/- warning: submodule.algebra_map_mem -> Submodule.algebraMap_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
-Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
 #align submodule.algebra_map_mem Submodule.algebraMap_mem
 
-/- warning: submodule.mem_one -> Submodule.mem_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
   Iff.rfl
@@ -153,56 +129,32 @@ theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
 -/
 
-/- warning: submodule.one_le -> Submodule.one_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) P) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) P)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) P) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) P)
-Case conversion may be inaccurate. Consider using '#align submodule.one_le Submodule.one_leₓ'. -/
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
   simpa only [one_eq_span, span_le, Set.singleton_subset_iff]
 #align submodule.one_le Submodule.one_le
 
-/- warning: submodule.map_one -> Submodule.map_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (OfNat.mk.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (One.one.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u1, u3} R _inst_1 A' _inst_4 _inst_5))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u2, u3} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))
-Case conversion may be inaccurate. Consider using '#align submodule.map_one Submodule.map_oneₓ'. -/
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (1 : Submodule R A) = 1 := by ext; simp
 #align submodule.map_one Submodule.map_one
 
-/- warning: submodule.map_op_one -> Submodule.map_op_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 := by ext;
   induction x using MulOpposite.rec'; simp
 #align submodule.map_op_one Submodule.map_op_one
 
-/- warning: submodule.comap_op_one -> Submodule.comap_op_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 := by ext;
   simp
 #align submodule.comap_op_one Submodule.comap_op_one
 
-/- warning: submodule.map_unop_one -> Submodule.map_unop_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_unop_one Submodule.map_unop_oneₓ'. -/
 @[simp]
 theorem map_unop_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R Aᵐᵒᵖ) = 1 := by
   rw [← comap_equiv_eq_map_symm, comap_op_one]
 #align submodule.map_unop_one Submodule.map_unop_one
 
-/- warning: submodule.comap_unop_one -> Submodule.comap_unop_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_one Submodule.comap_unop_oneₓ'. -/
 @[simp]
 theorem comap_unop_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R A) = 1 := by
@@ -214,29 +166,14 @@ smallest R-submodule of `A` containing the elements `m * n` for `m ∈ M` and `n
 instance : Mul (Submodule R A) :=
   ⟨Submodule.map₂ <| LinearMap.mul R A⟩
 
-/- warning: submodule.mul_mem_mul -> Submodule.mul_mem_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
-Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul Submodule.mul_mem_mulₓ'. -/
 theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
   apply_mem_map₂ _ hm hn
 #align submodule.mul_mem_mul Submodule.mul_mem_mul
 
-/- warning: submodule.mul_le -> Submodule.mul_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_le Submodule.mul_leₓ'. -/
 theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
   map₂_le
 #align submodule.mul_le Submodule.mul_le
 
-/- warning: submodule.mul_to_add_submonoid -> Submodule.mul_toAddSubmonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHMul.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) N))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHMul.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.mul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) N))
-Case conversion may be inaccurate. Consider using '#align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoidₓ'. -/
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid :=
   by
@@ -247,9 +184,6 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
 
-/- warning: submodule.mul_induction_on -> Submodule.mul_induction_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on Submodule.mul_induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
     (hm : ∀ m ∈ M, ∀ n ∈ N, C (m * n)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -258,9 +192,6 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
   exact AddSubmonoid.mul_induction_on hr hm ha
 #align submodule.mul_induction_on Submodule.mul_induction_on
 
-/- warning: submodule.mul_induction_on' -> Submodule.mul_induction_on' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on' Submodule.mul_induction_on'ₓ'. -/
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
 protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
@@ -275,12 +206,6 @@ protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
 
 variable (R)
 
-/- warning: submodule.span_mul_span -> Submodule.span_mul_span is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} A) (T : Set.{u2} A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) S T))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} A) (T : Set.{u2} A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) S T))
-Case conversion may be inaccurate. Consider using '#align submodule.span_mul_span Submodule.span_mul_spanₓ'. -/
 theorem span_mul_span : span R S * span R T = span R (S * T) :=
   map₂_span_span _ _ _ _
 #align submodule.span_mul_span Submodule.span_mul_span
@@ -296,12 +221,6 @@ theorem mul_bot : M * ⊥ = ⊥ :=
 #align submodule.mul_bot Submodule.mul_bot
 -/
 
-/- warning: submodule.bot_mul -> Submodule.bot_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasBot.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasBot.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instBotSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instBotSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
-Case conversion may be inaccurate. Consider using '#align submodule.bot_mul Submodule.bot_mulₓ'. -/
 @[simp]
 theorem bot_mul : ⊥ * M = ⊥ :=
   map₂_bot_left _ _
@@ -323,24 +242,15 @@ protected theorem mul_one : M * 1 = M := by conv_lhs => rw [one_eq_span, ← spa
 
 variable {M N P Q}
 
-/- warning: submodule.mul_le_mul -> Submodule.mul_le_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul Submodule.mul_le_mulₓ'. -/
 @[mono]
 theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
   map₂_le_map₂ hmp hnq
 #align submodule.mul_le_mul Submodule.mul_le_mul
 
-/- warning: submodule.mul_le_mul_left -> Submodule.mul_le_mul_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_left Submodule.mul_le_mul_leftₓ'. -/
 theorem mul_le_mul_left (h : M ≤ N) : M * P ≤ N * P :=
   map₂_le_map₂_left h
 #align submodule.mul_le_mul_left Submodule.mul_le_mul_left
 
-/- warning: submodule.mul_le_mul_right -> Submodule.mul_le_mul_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_right Submodule.mul_le_mul_rightₓ'. -/
 theorem mul_le_mul_right (h : N ≤ P) : M * N ≤ M * P :=
   map₂_le_map₂_right h
 #align submodule.mul_le_mul_right Submodule.mul_le_mul_right
@@ -353,23 +263,14 @@ theorem mul_sup : M * (N ⊔ P) = M * N ⊔ M * P :=
 #align submodule.mul_sup Submodule.mul_sup
 -/
 
-/- warning: submodule.sup_mul -> Submodule.sup_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.sup_mul Submodule.sup_mulₓ'. -/
 theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
   map₂_sup_left _ _ _ _
 #align submodule.sup_mul Submodule.sup_mul
 
-/- warning: submodule.mul_subset_mul -> Submodule.mul_subset_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_subset_mul Submodule.mul_subset_mulₓ'. -/
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
   image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
-/- warning: submodule.map_mul -> Submodule.map_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_mul Submodule.map_mulₓ'. -/
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
   calc
@@ -393,9 +294,6 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
     
 #align submodule.map_mul Submodule.map_mul
 
-/- warning: submodule.map_op_mul -> Submodule.map_op_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_op_mul Submodule.map_op_mulₓ'. -/
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
@@ -412,9 +310,6 @@ theorem map_op_mul :
     exact mul_mem_mul hn hm
 #align submodule.map_op_mul Submodule.map_op_mul
 
-/- warning: submodule.comap_unop_mul -> Submodule.comap_unop_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_mul Submodule.comap_unop_mulₓ'. -/
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
@@ -422,9 +317,6 @@ theorem comap_unop_mul :
   by simp_rw [← map_equiv_eq_comap_symm, map_op_mul]
 #align submodule.comap_unop_mul Submodule.comap_unop_mul
 
-/- warning: submodule.map_unop_mul -> Submodule.map_unop_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_unop_mul Submodule.map_unop_mulₓ'. -/
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
@@ -436,9 +328,6 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
       LinearEquiv.symm_trans_self, LinearEquiv.refl_toLinearMap, map_id, map_id, map_id]
 #align submodule.map_unop_mul Submodule.map_unop_mul
 
-/- warning: submodule.comap_op_mul -> Submodule.comap_op_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_op_mul Submodule.comap_op_mulₓ'. -/
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
@@ -467,12 +356,6 @@ section DecidableEq
 
 open Classical
 
-/- warning: submodule.mem_span_mul_finite_of_mem_span_mul -> Submodule.mem_span_mul_finite_of_mem_span_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : AddCommMonoid.{u2} A] [_inst_6 : Mul.{u2} A] [_inst_7 : Module.{u1, u2} R A _inst_4 _inst_5] {S : Set.{u2} A} {S' : Set.{u2} A} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) S S'))) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) S) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') S') (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
-but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} A] [_inst_6 : Mul.{u1} A] [_inst_7 : Module.{u2, u1} R A _inst_4 _inst_5] {S : Set.{u1} A} {S' : Set.{u1} A} {x : A}, (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) S S'))) -> (Exists.{succ u1} (Finset.{u1} A) (fun (T : Finset.{u1} A) => Exists.{succ u1} (Finset.{u1} A) (fun (T' : Finset.{u1} A) => And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T) S) (And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T') S') (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) (Finset.toSet.{u1} A T) (Finset.toSet.{u1} A T'))))))))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_span_mul Submodule.mem_span_mul_finite_of_mem_span_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :
     ∃ T T' : Finset A, ↑T ⊆ S ∧ ↑T' ⊆ S' ∧ x ∈ span R (T * T' : Set A) :=
@@ -487,19 +370,10 @@ theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A]
 
 end DecidableEq
 
-/- warning: submodule.mul_eq_span_mul_set -> Submodule.mul_eq_span_mul_set is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) t)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) t)))
-Case conversion may be inaccurate. Consider using '#align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_setₓ'. -/
 theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A) * (t : Set A)) :=
   map₂_eq_span_image2 _ s t
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
 
-/- warning: submodule.supr_mul -> Submodule.iSup_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.supr_mul Submodule.iSup_mulₓ'. -/
 theorem iSup_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
   map₂_iSup_left _ s t
 #align submodule.supr_mul Submodule.iSup_mul
@@ -510,9 +384,6 @@ theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s
 #align submodule.mul_supr Submodule.mul_iSup
 -/
 
-/- warning: submodule.mem_span_mul_finite_of_mem_mul -> Submodule.mem_span_mul_finite_of_mem_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
   Submodule.mem_span_mul_finite_of_mem_span_mul
@@ -521,22 +392,10 @@ theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈
 
 variable {M N P}
 
-/- warning: submodule.mem_span_singleton_mul -> Submodule.mem_span_singleton_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) y z) x)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) y z) x)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mulₓ'. -/
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x := by
   simp_rw [(· * ·), map₂_span_singleton_eq_map, exists_prop]; rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
 
-/- warning: submodule.mem_mul_span_singleton -> Submodule.mem_mul_span_singleton is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) z y) x)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) z y) x)))
-Case conversion may be inaccurate. Consider using '#align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singletonₓ'. -/
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x := by
   simp_rw [(· * ·), map₂_span_singleton_eq_map_flip, exists_prop]; rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
@@ -570,9 +429,6 @@ theorem pow_eq_span_pow_set (n : ℕ) : M ^ n = span R ((M : Set A) ^ n) := by
 #align submodule.pow_eq_span_pow_set Submodule.pow_eq_span_pow_set
 -/
 
-/- warning: submodule.pow_subset_pow -> Submodule.pow_subset_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.pow_subset_pow Submodule.pow_subset_powₓ'. -/
 theorem pow_subset_pow {n : ℕ} : (↑M : Set A) ^ n ⊆ ↑(M ^ n : Submodule R A) :=
   (pow_eq_span_pow_set M n).symm ▸ subset_span
 #align submodule.pow_subset_pow Submodule.pow_subset_pow
@@ -595,9 +451,6 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
 #align submodule.pow_to_add_submonoid Submodule.pow_toAddSubmonoid
 -/
 
-/- warning: submodule.le_pow_to_add_submonoid -> Submodule.le_pow_toAddSubmonoid is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoidₓ'. -/
 theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAddSubmonoid :=
   by
   obtain rfl | hn := Decidable.eq_or_ne n 0
@@ -605,9 +458,6 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
   · exact (pow_to_add_submonoid M hn).ge
 #align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoid
 
-/- warning: submodule.pow_induction_on_left' -> Submodule.pow_induction_on_left' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -625,9 +475,6 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'
 
-/- warning: submodule.pow_induction_on_right' -> Submodule.pow_induction_on_right' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -649,9 +496,6 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'
 
-/- warning: submodule.pow_induction_on_left -> Submodule.pow_induction_on_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -662,9 +506,6 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
     (fun m hm i x hx => hmul _ hm _) hx
 #align submodule.pow_induction_on_left Submodule.pow_induction_on_left
 
-/- warning: submodule.pow_induction_on_right -> Submodule.pow_induction_on_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -686,9 +527,6 @@ def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R
 #align submodule.map_hom Submodule.mapHom
 -/
 
-/- warning: submodule.equiv_opposite -> Submodule.equivOpposite is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.equiv_opposite Submodule.equivOppositeₓ'. -/
 /-- The ring of submodules of the opposite algebra is isomorphic to the opposite ring of
 submodules. -/
 @[simps apply symm_apply]
@@ -702,56 +540,35 @@ def equivOpposite : Submodule R Aᵐᵒᵖ ≃+* (Submodule R A)ᵐᵒᵖ
   map_mul' p q := congr_arg op <| comap_op_mul _ _
 #align submodule.equiv_opposite Submodule.equivOpposite
 
-/- warning: submodule.map_pow -> Submodule.map_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_pow Submodule.map_powₓ'. -/
 protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') (n : ℕ) :
     map f.toLinearMap (M ^ n) = map f.toLinearMap M ^ n :=
   map_pow (mapHom f) M n
 #align submodule.map_pow Submodule.map_pow
 
-/- warning: submodule.comap_unop_pow -> Submodule.comap_unop_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_pow Submodule.comap_unop_powₓ'. -/
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).symm.map_pow (op M) n
 #align submodule.comap_unop_pow Submodule.comap_unop_pow
 
-/- warning: submodule.comap_op_pow -> Submodule.comap_op_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.comap_op_pow Submodule.comap_op_powₓ'. -/
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   op_injective <| (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).map_pow M n
 #align submodule.comap_op_pow Submodule.comap_op_pow
 
-/- warning: submodule.map_op_pow -> Submodule.map_op_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_op_pow Submodule.map_op_powₓ'. -/
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   by rw [map_equiv_eq_comap_symm, map_equiv_eq_comap_symm, comap_unop_pow]
 #align submodule.map_op_pow Submodule.map_op_pow
 
-/- warning: submodule.map_unop_pow -> Submodule.map_unop_pow is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_unop_pow Submodule.map_unop_powₓ'. -/
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   by rw [← comap_equiv_eq_map_symm, ← comap_equiv_eq_map_symm, comap_op_pow]
 #align submodule.map_unop_pow Submodule.map_unop_pow
 
-/- warning: submodule.span.ring_hom -> Submodule.span.ringHom is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingHom.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetSemiring.nonAssocSemiring.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingHom.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetSemiring.instNonAssocSemiringSetSemiring.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
-Case conversion may be inaccurate. Consider using '#align submodule.span.ring_hom Submodule.span.ringHomₓ'. -/
 /-- `span` is a semiring homomorphism (recall multiplication is pointwise multiplication of subsets
 on either side). -/
 @[simps]
@@ -768,12 +585,6 @@ section
 
 variable {α : Type _} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A]
 
-/- warning: submodule.pointwise_mul_semiring_action -> Submodule.pointwiseMulSemiringAction is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} [_inst_4 : Monoid.{u3} α] [_inst_5 : MulSemiringAction.{u3, u2} α A _inst_4 _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} α R A (SMulZeroClass.toHasSmul.{u3, u2} α A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} α A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} α A _inst_4 (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} α A _inst_4 _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], MulSemiringAction.{u3, u2} α (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_4 (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} [_inst_4 : Monoid.{u3} α] [_inst_5 : MulSemiringAction.{u3, u2} α A _inst_4 _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} α R A (SMulZeroClass.toSMul.{u3, u2} α A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} α A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} α A _inst_4 (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} α A _inst_4 _inst_2 _inst_5)))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], MulSemiringAction.{u3, u2} α (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_4 (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))
-Case conversion may be inaccurate. Consider using '#align submodule.pointwise_mul_semiring_action Submodule.pointwiseMulSemiringActionₓ'. -/
 /-- The action on a submodule corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale.
@@ -798,9 +609,6 @@ variable {A : Type v} [CommSemiring A] [Algebra R A]
 
 variable {M N : Submodule R A} {m n : A}
 
-/- warning: submodule.mul_mem_mul_rev -> Submodule.mul_mem_mul_rev is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_revₓ'. -/
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=
   mul_comm m n ▸ mul_mem_mul hm hn
 #align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_rev
@@ -818,12 +626,6 @@ protected theorem mul_comm : M * N = N * M :=
 instance : IdemCommSemiring (Submodule R A) :=
   { Submodule.idemSemiring with mul_comm := Submodule.mul_comm }
 
-/- warning: submodule.prod_span -> Submodule.prod_span is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (M : ι -> (Set.{u2} A)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Finset.prod.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.idemCommSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (M i))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Finset.prod.{u2, u3} (Set.{u2} A) ι (Set.commMonoid.{u2} A (CommSemiring.toCommMonoid.{u2} A _inst_2)) s (fun (i : ι) => M i)))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (M : ι -> (Set.{u3} A)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Finset.prod.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (M i))) (Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Finset.prod.{u3, u1} (Set.{u3} A) ι (Set.commMonoid.{u3} A (CommSemiring.toCommMonoid.{u3} A _inst_2)) s (fun (i : ι) => M i)))
-Case conversion may be inaccurate. Consider using '#align submodule.prod_span Submodule.prod_spanₓ'. -/
 theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     (∏ i in s, Submodule.span R (M i)) = Submodule.span R (∏ i in s, M i) :=
   by
@@ -834,12 +636,6 @@ theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     rw [Finset.prod_insert H, Finset.prod_insert H, ih, span_mul_span]
 #align submodule.prod_span Submodule.prod_span
 
-/- warning: submodule.prod_span_singleton -> Submodule.prod_span_singleton is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (x : ι -> A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Finset.prod.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.idemCommSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (x i)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (Finset.prod.{u2, u3} A ι (CommSemiring.toCommMonoid.{u2} A _inst_2) s (fun (i : ι) => x i))))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (x : ι -> A), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Finset.prod.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.instSingletonSet.{u3} A) (x i)))) (Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.instSingletonSet.{u3} A) (Finset.prod.{u3, u1} A ι (CommSemiring.toCommMonoid.{u3} A _inst_2) s (fun (i : ι) => x i))))
-Case conversion may be inaccurate. Consider using '#align submodule.prod_span_singleton Submodule.prod_span_singletonₓ'. -/
 theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
     (∏ i in s, span R ({x i} : Set A)) = span R {∏ i in s, x i} := by
   rw [prod_span, Set.finset_prod_singleton]
@@ -847,12 +643,6 @@ theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
 
 variable (R A)
 
-/- warning: submodule.module_set -> Submodule.moduleSet is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Module.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemSemiring.toSemiring.{u2} (SetSemiring.{u2} A) (SetSemiring.idemSemiring.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Module.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemSemiring.toSemiring.{u2} (SetSemiring.{u2} A) (SetSemiring.instIdemSemiringSetSemiring.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))
-Case conversion may be inaccurate. Consider using '#align submodule.module_set Submodule.moduleSetₓ'. -/
 /-- R-submodules of the R-algebra A are a module over `set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A)
     where
@@ -915,38 +705,23 @@ instance : Div (Submodule R A) :=
         rw [Algebra.smul_mul_assoc]
         exact Submodule.smul_mem _ _ (hx _ hy) }⟩
 
-/- warning: submodule.mem_div_iff_forall_mul_mem -> Submodule.mem_div_iff_forall_mul_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_memₓ'. -/
 theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I :=
   Iff.refl _
 #align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_mem
 
-/- warning: submodule.mem_div_iff_smul_subset -> Submodule.mem_div_iff_smul_subset is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subsetₓ'. -/
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
   ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by rw [← xy'_eq_y]; apply h; assumption, fun h y hy =>
     h (Set.smul_mem_smul_set hy)⟩
 #align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subset
 
-/- warning: submodule.le_div_iff -> Submodule.le_div_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff Submodule.le_div_iffₓ'. -/
 theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z ∈ K, x * z ∈ J :=
   Iff.refl _
 #align submodule.le_div_iff Submodule.le_div_iff
 
-/- warning: submodule.le_div_iff_mul_le -> Submodule.le_div_iff_mul_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J := by
   rw [le_div_iff, mul_le]
 #align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_le
 
-/- warning: submodule.one_le_one_div -> Submodule.one_le_one_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.one_le_one_div Submodule.one_le_one_divₓ'. -/
 @[simp]
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   by
@@ -955,9 +730,6 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   · rwa [le_div_iff_mul_le, one_mul]
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
-/- warning: submodule.le_self_mul_one_div -> Submodule.le_self_mul_one_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.le_self_mul_one_div Submodule.le_self_mul_one_divₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
   by
@@ -965,9 +737,6 @@ theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 /
   apply mul_le_mul_right (one_le_one_div.mpr hI)
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
 
-/- warning: submodule.mul_one_div_le_one -> Submodule.mul_one_div_le_one is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.mul_one_div_le_one Submodule.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
@@ -977,9 +746,6 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
 
-/- warning: submodule.map_div -> Submodule.map_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align submodule.map_div Submodule.map_divₓ'. -/
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)
     (h : A ≃ₐ[R] B) : (I / J).map h.toLinearMap = I.map h.toLinearMap / J.map h.toLinearMap :=

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

@@ -170,10 +170,7 @@ but is expected to have type
   forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u2, u3} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_one Submodule.map_oneₓ'. -/
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
-    map f.toLinearMap (1 : Submodule R A) = 1 :=
-  by
-  ext
-  simp
+    map f.toLinearMap (1 : Submodule R A) = 1 := by ext; simp
 #align submodule.map_one Submodule.map_one
 
 /- warning: submodule.map_op_one -> Submodule.map_op_one is a dubious translation:
@@ -181,11 +178,8 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
-    map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 :=
-  by
-  ext
-  induction x using MulOpposite.rec'
-  simp
+    map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 := by ext;
+  induction x using MulOpposite.rec'; simp
 #align submodule.map_op_one Submodule.map_op_one
 
 /- warning: submodule.comap_op_one -> Submodule.comap_op_one is a dubious translation:
@@ -193,9 +187,7 @@ theorem map_op_one :
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
-    comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 :=
-  by
-  ext
+    comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 := by ext;
   simp
 #align submodule.comap_op_one Submodule.comap_op_one
 
@@ -317,18 +309,14 @@ theorem bot_mul : ⊥ * M = ⊥ :=
 
 #print Submodule.one_mul /-
 @[simp]
-protected theorem one_mul : (1 : Submodule R A) * M = M :=
-  by
-  conv_lhs => rw [one_eq_span, ← span_eq M]
-  erw [span_mul_span, one_mul, span_eq]
+protected theorem one_mul : (1 : Submodule R A) * M = M := by
+  conv_lhs => rw [one_eq_span, ← span_eq M]; erw [span_mul_span, one_mul, span_eq]
 #align submodule.one_mul Submodule.one_mul
 -/
 
 #print Submodule.mul_one /-
 @[simp]
-protected theorem mul_one : M * 1 = M :=
-  by
-  conv_lhs => rw [one_eq_span, ← span_eq M]
+protected theorem mul_one : M * 1 = M := by conv_lhs => rw [one_eq_span, ← span_eq M];
   erw [span_mul_span, mul_one, span_eq]
 #align submodule.mul_one Submodule.mul_one
 -/
@@ -539,10 +527,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) y z) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mulₓ'. -/
-theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x :=
-  by
-  simp_rw [(· * ·), map₂_span_singleton_eq_map, exists_prop]
-  rfl
+theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x := by
+  simp_rw [(· * ·), map₂_span_singleton_eq_map, exists_prop]; rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
 
 /- warning: submodule.mem_mul_span_singleton -> Submodule.mem_mul_span_singleton is a dubious translation:
@@ -551,10 +537,8 @@ lean 3 declaration is
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) z y) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singletonₓ'. -/
-theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x :=
-  by
-  simp_rw [(· * ·), map₂_span_singleton_eq_map_flip, exists_prop]
-  rfl
+theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x := by
+  simp_rw [(· * ·), map₂_span_singleton_eq_map_flip, exists_prop]; rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
 
 /-- Sub-R-modules of an R-algebra form an idempotent semiring. -/
@@ -617,8 +601,7 @@ Case conversion may be inaccurate. Consider using '#align submodule.le_pow_to_ad
 theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAddSubmonoid :=
   by
   obtain rfl | hn := Decidable.eq_or_ne n 0
-  · rw [pow_zero, pow_zero]
-    exact le_one_to_add_submonoid
+  · rw [pow_zero, pow_zero]; exact le_one_to_add_submonoid
   · exact (pow_to_add_submonoid M hn).ge
 #align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoid
 
@@ -909,8 +892,7 @@ theorem smul_singleton (a : A) (M : Submodule R A) :
     rintro _ ⟨b, m, hb, hm, rfl⟩
     rw [SetLike.mem_coe, mem_map, set.mem_singleton_iff.mp hb]
     exact ⟨m, hm, rfl⟩
-  · rintro _ ⟨m, hm, rfl⟩
-    exact subset_span ⟨a, m, Set.mem_singleton a, hm, rfl⟩
+  · rintro _ ⟨m, hm, rfl⟩; exact subset_span ⟨a, m, Set.mem_singleton a, hm, rfl⟩
 #align submodule.smul_singleton Submodule.smul_singleton
 -/
 
@@ -926,11 +908,8 @@ This is the general form of the ideal quotient, traditionally written $I : J$.
 instance : Div (Submodule R A) :=
   ⟨fun I J =>
     { carrier := { x | ∀ y ∈ J, x * y ∈ I }
-      zero_mem' := fun y hy => by
-        rw [MulZeroClass.zero_mul]
-        apply Submodule.zero_mem
-      add_mem' := fun a b ha hb y hy => by
-        rw [add_mul]
+      zero_mem' := fun y hy => by rw [MulZeroClass.zero_mul]; apply Submodule.zero_mem
+      add_mem' := fun a b ha hb y hy => by rw [add_mul];
         exact Submodule.add_mem _ (ha _ hy) (hb _ hy)
       smul_mem' := fun r x hx y hy => by
         rw [Algebra.smul_mul_assoc]
@@ -947,10 +926,8 @@ theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J 
 <too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subsetₓ'. -/
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
-  ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by
-    rw [← xy'_eq_y]
-    apply h
-    assumption, fun h y hy => h (Set.smul_mem_smul_set hy)⟩
+  ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by rw [← xy'_eq_y]; apply h; assumption, fun h y hy =>
+    h (Set.smul_mem_smul_set hy)⟩
 #align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subset
 
 /- warning: submodule.le_div_iff -> Submodule.le_div_iff is a dubious translation:

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

@@ -61,20 +61,14 @@ namespace SubMulAction
 variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 
 /- warning: sub_mul_action.algebra_map_mem -> SubMulAction.algebraMap_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
 #align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_mem
 
 /- warning: sub_mul_action.mem_one' -> SubMulAction.mem_one' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
@@ -183,10 +177,7 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 #align submodule.map_one Submodule.map_one
 
 /- warning: submodule.map_op_one -> Submodule.map_op_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
@@ -198,10 +189,7 @@ theorem map_op_one :
 #align submodule.map_op_one Submodule.map_op_one
 
 /- warning: submodule.comap_op_one -> Submodule.comap_op_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
@@ -212,10 +200,7 @@ theorem comap_op_one :
 #align submodule.comap_op_one Submodule.comap_op_one
 
 /- warning: submodule.map_unop_one -> Submodule.map_unop_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_one Submodule.map_unop_oneₓ'. -/
 @[simp]
 theorem map_unop_one :
@@ -224,10 +209,7 @@ theorem map_unop_one :
 #align submodule.map_unop_one Submodule.map_unop_one
 
 /- warning: submodule.comap_unop_one -> Submodule.comap_unop_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_one Submodule.comap_unop_oneₓ'. -/
 @[simp]
 theorem comap_unop_one :
@@ -251,10 +233,7 @@ theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
 #align submodule.mul_mem_mul Submodule.mul_mem_mul
 
 /- warning: submodule.mul_le -> Submodule.mul_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) P)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) P)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le Submodule.mul_leₓ'. -/
 theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
   map₂_le
@@ -277,10 +256,7 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
 
 /- warning: submodule.mul_induction_on -> Submodule.mul_induction_on is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on Submodule.mul_induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
@@ -291,10 +267,7 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
 #align submodule.mul_induction_on Submodule.mul_induction_on
 
 /- warning: submodule.mul_induction_on' -> Submodule.mul_induction_on' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on' Submodule.mul_induction_on'ₓ'. -/
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
@@ -363,10 +336,7 @@ protected theorem mul_one : M * 1 = M :=
 variable {M N P Q}
 
 /- warning: submodule.mul_le_mul -> Submodule.mul_le_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N Q) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N Q) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul Submodule.mul_le_mulₓ'. -/
 @[mono]
 theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
@@ -374,20 +344,14 @@ theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
 #align submodule.mul_le_mul Submodule.mul_le_mul
 
 /- warning: submodule.mul_le_mul_left -> Submodule.mul_le_mul_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_left Submodule.mul_le_mul_leftₓ'. -/
 theorem mul_le_mul_left (h : M ≤ N) : M * P ≤ N * P :=
   map₂_le_map₂_left h
 #align submodule.mul_le_mul_left Submodule.mul_le_mul_left
 
 /- warning: submodule.mul_le_mul_right -> Submodule.mul_le_mul_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_right Submodule.mul_le_mul_rightₓ'. -/
 theorem mul_le_mul_right (h : N ≤ P) : M * N ≤ M * P :=
   map₂_le_map₂_right h
@@ -402,30 +366,21 @@ theorem mul_sup : M * (N ⊔ P) = M * N ⊔ M * P :=
 -/
 
 /- warning: submodule.sup_mul -> Submodule.sup_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) P) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) P) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.sup_mul Submodule.sup_mulₓ'. -/
 theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
   map₂_sup_left _ _ _ _
 #align submodule.sup_mul Submodule.sup_mul
 
 /- warning: submodule.mul_subset_mul -> Submodule.mul_subset_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) N)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) N)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_subset_mul Submodule.mul_subset_mulₓ'. -/
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
   image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
 /- warning: submodule.map_mul -> Submodule.map_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u3, u3, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u1, u3} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u2, u1} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_mul Submodule.map_mulₓ'. -/
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
@@ -451,10 +406,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 #align submodule.map_mul Submodule.map_mul
 
 /- warning: submodule.map_op_mul -> Submodule.map_op_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_mul Submodule.map_op_mulₓ'. -/
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -473,10 +425,7 @@ theorem map_op_mul :
 #align submodule.map_op_mul Submodule.map_op_mul
 
 /- warning: submodule.comap_unop_mul -> Submodule.comap_unop_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_mul Submodule.comap_unop_mulₓ'. -/
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -486,10 +435,7 @@ theorem comap_unop_mul :
 #align submodule.comap_unop_mul Submodule.comap_unop_mul
 
 /- warning: submodule.map_unop_mul -> Submodule.map_unop_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_mul Submodule.map_unop_mulₓ'. -/
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -503,10 +449,7 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
 #align submodule.map_unop_mul Submodule.map_unop_mul
 
 /- warning: submodule.comap_op_mul -> Submodule.comap_op_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_mul Submodule.comap_op_mulₓ'. -/
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -567,10 +510,7 @@ theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A)
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
 
 /- warning: submodule.supr_mul -> Submodule.iSup_mul is a dubious translation:
-lean 3 declaration is
-  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
-but is expected to have type
-  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.supr_mul Submodule.iSup_mulₓ'. -/
 theorem iSup_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
   map₂_iSup_left _ s t
@@ -583,10 +523,7 @@ theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s
 -/
 
 /- warning: submodule.mem_span_mul_finite_of_mem_mul -> Submodule.mem_span_mul_finite_of_mem_mul is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) Q)) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T') (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Q)) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Finset.toSet.{u2} A T) (Finset.toSet.{u2} A T'))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
@@ -650,10 +587,7 @@ theorem pow_eq_span_pow_set (n : ℕ) : M ^ n = span R ((M : Set A) ^ n) := by
 -/
 
 /- warning: submodule.pow_subset_pow -> Submodule.pow_subset_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (Semiring.toOne.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) n) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.pow_subset_pow Submodule.pow_subset_powₓ'. -/
 theorem pow_subset_pow {n : ℕ} : (↑M : Set A) ^ n ⊆ ↑(M ^ n : Submodule R A) :=
   (pow_eq_span_pow_set M n).symm ▸ subset_span
@@ -678,10 +612,7 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
 -/
 
 /- warning: submodule.le_pow_to_add_submonoid -> Submodule.le_pow_toAddSubmonoid is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toHasLe.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoidₓ'. -/
 theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAddSubmonoid :=
   by
@@ -692,10 +623,7 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 #align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoid
 
 /- warning: submodule.pow_induction_on_left' -> Submodule.pow_induction_on_left' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
@@ -715,10 +643,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 #align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'
 
 /- warning: submodule.pow_induction_on_right' -> Submodule.pow_induction_on_right' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5914 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
@@ -742,10 +667,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
 #align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'
 
 /- warning: submodule.pow_induction_on_left -> Submodule.pow_induction_on_left is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
@@ -758,10 +680,7 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
 #align submodule.pow_induction_on_left Submodule.pow_induction_on_left
 
 /- warning: submodule.pow_induction_on_right -> Submodule.pow_induction_on_right is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/
@@ -785,10 +704,7 @@ def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R
 -/
 
 /- warning: submodule.equiv_opposite -> Submodule.equivOpposite is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.hasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (MulOpposite.hasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.add.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.equiv_opposite Submodule.equivOppositeₓ'. -/
 /-- The ring of submodules of the opposite algebra is isomorphic to the opposite ring of
 submodules. -/
@@ -804,10 +720,7 @@ def equivOpposite : Submodule R Aᵐᵒᵖ ≃+* (Submodule R A)ᵐᵒᵖ
 #align submodule.equiv_opposite Submodule.equivOpposite
 
 /- warning: submodule.map_pow -> Submodule.map_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u3, 0, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u3, 0} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u1, u3} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u3, 0, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u3, 0} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u2, u3} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u1, 0} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_pow Submodule.map_powₓ'. -/
 protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') (n : ℕ) :
     map f.toLinearMap (M ^ n) = map f.toLinearMap M ^ n :=
@@ -815,10 +728,7 @@ protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 #align submodule.map_pow Submodule.map_pow
 
 /- warning: submodule.comap_unop_pow -> Submodule.comap_unop_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_pow Submodule.comap_unop_powₓ'. -/
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
@@ -827,10 +737,7 @@ theorem comap_unop_pow (n : ℕ) :
 #align submodule.comap_unop_pow Submodule.comap_unop_pow
 
 /- warning: submodule.comap_op_pow -> Submodule.comap_op_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_pow Submodule.comap_op_powₓ'. -/
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -839,10 +746,7 @@ theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 #align submodule.comap_op_pow Submodule.comap_op_pow
 
 /- warning: submodule.map_op_pow -> Submodule.map_op_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_pow Submodule.map_op_powₓ'. -/
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -851,10 +755,7 @@ theorem map_op_pow (n : ℕ) :
 #align submodule.map_op_pow Submodule.map_op_pow
 
 /- warning: submodule.map_unop_pow -> Submodule.map_unop_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_pow Submodule.map_unop_powₓ'. -/
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
@@ -915,10 +816,7 @@ variable {A : Type v} [CommSemiring A] [Algebra R A]
 variable {M N : Submodule R A} {m n : A}
 
 /- warning: submodule.mul_mem_mul_rev -> Submodule.mul_mem_mul_rev is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_revₓ'. -/
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=
   mul_comm m n ▸ mul_mem_mul hm hn
@@ -1039,20 +937,14 @@ instance : Div (Submodule R A) :=
         exact Submodule.smul_mem _ _ (hx _ hy) }⟩
 
 /- warning: submodule.mem_div_iff_forall_mul_mem -> Submodule.mem_div_iff_forall_mul_mem is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x y) I))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x y) I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_memₓ'. -/
 theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I :=
   Iff.refl _
 #align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_mem
 
 /- warning: submodule.mem_div_iff_smul_subset -> Submodule.mem_div_iff_smul_subset is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (SMul.smul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Mul.toSMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) J)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) I))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HSMul.hSMul.{u2, u2, u2} A (Set.{u2} A) (Set.{u2} A) (instHSMul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Algebra.toSMul.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)))) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) J)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subsetₓ'. -/
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
   ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by
@@ -1062,30 +954,21 @@ theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔
 #align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subset
 
 /- warning: submodule.le_div_iff -> Submodule.le_div_iff is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x z) J)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x z) J)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff Submodule.le_div_iffₓ'. -/
 theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z ∈ K, x * z ∈ J :=
   Iff.refl _
 #align submodule.le_div_iff Submodule.le_div_iff
 
 /- warning: submodule.le_div_iff_mul_le -> Submodule.le_div_iff_mul_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J := by
   rw [le_div_iff, mul_le]
 #align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_le
 
 /- warning: submodule.one_le_one_div -> Submodule.one_le_one_div is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.one_le_one_div Submodule.one_le_one_divₓ'. -/
 @[simp]
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
@@ -1096,10 +979,7 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
 /- warning: submodule.le_self_mul_one_div -> Submodule.le_self_mul_one_div is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.le_self_mul_one_div Submodule.le_self_mul_one_divₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
@@ -1109,10 +989,7 @@ theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 /
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
 
 /- warning: submodule.mul_one_div_le_one -> Submodule.mul_one_div_le_one is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.mul_one_div_le_one Submodule.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
@@ -1124,10 +1001,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
 
 /- warning: submodule.map_div -> Submodule.map_div is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {B : Type.{u3}} [_inst_4 : CommSemiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4)] (I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (h : AlgEquiv.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (instHDiv.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.hasDiv.{u1, u3} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) J))
-but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {B : Type.{u1}} [_inst_4 : CommSemiring.{u1} B] [_inst_5 : Algebra.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4)] (I : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (J : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (h : AlgEquiv.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (instHDiv.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (instHDiv.{u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) J))
+<too large>
 Case conversion may be inaccurate. Consider using '#align submodule.map_div Submodule.map_divₓ'. -/
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -718,7 +718,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5912 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5914 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5913) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -64,7 +64,7 @@ variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
@@ -74,7 +74,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
@@ -120,7 +120,7 @@ theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
@@ -130,7 +130,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
@@ -695,7 +695,7 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
@@ -718,7 +718,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5912 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5912 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
@@ -745,7 +745,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
@@ -761,7 +761,7 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -98,15 +98,11 @@ variable (S T : Set A) {M N P Q : Submodule R A} {m n : A}
 instance : One (Submodule R A) :=
   ⟨(Algebra.linearMap R A).range⟩
 
-/- warning: submodule.one_eq_range -> Submodule.one_eq_range is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (LinearMap.range.{u1, u1, u1, u2, max u1 u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.linearMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (LinearMap.range.{u1, u1, u1, u2, max u1 u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.linearMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))
-Case conversion may be inaccurate. Consider using '#align submodule.one_eq_range Submodule.one_eq_rangeₓ'. -/
+#print Submodule.one_eq_range /-
 theorem one_eq_range : (1 : Submodule R A) = (Algebra.linearMap R A).range :=
   rfl
 #align submodule.one_eq_range Submodule.one_eq_range
+-/
 
 /- warning: submodule.le_one_to_add_submonoid -> Submodule.le_one_toAddSubmonoid is a dubious translation:
 lean 3 declaration is
@@ -177,7 +173,7 @@ theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (OfNat.mk.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (One.one.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u1, u3} R _inst_1 A' _inst_4 _inst_5))))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u2, u3} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u2, u3} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_one Submodule.map_oneₓ'. -/
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (1 : Submodule R A) = 1 :=
@@ -190,7 +186,7 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
@@ -205,7 +201,7 @@ theorem map_op_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
@@ -219,7 +215,7 @@ theorem comap_op_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_one Submodule.map_unop_oneₓ'. -/
 @[simp]
 theorem map_unop_one :
@@ -231,7 +227,7 @@ theorem map_unop_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_one Submodule.comap_unop_oneₓ'. -/
 @[simp]
 theorem comap_unop_one :
@@ -429,7 +425,7 @@ theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u3, u3, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u1, u3} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u2, u1} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u2, u1} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
 Case conversion may be inaccurate. Consider using '#align submodule.map_mul Submodule.map_mulₓ'. -/
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
@@ -458,7 +454,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_mul Submodule.map_op_mulₓ'. -/
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -480,7 +476,7 @@ theorem map_op_mul :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_mul Submodule.comap_unop_mulₓ'. -/
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -493,7 +489,7 @@ theorem comap_unop_mul :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_mul Submodule.map_unop_mulₓ'. -/
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -510,7 +506,7 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_mul Submodule.comap_op_mulₓ'. -/
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -811,7 +807,7 @@ def equivOpposite : Submodule R Aᵐᵒᵖ ≃+* (Submodule R A)ᵐᵒᵖ
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u3, 0, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u3, 0} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u1, u3} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u3, 0, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u3, 0} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u2, u3} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u1, 0} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u3, 0, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u3, 0} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u2, u3} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u1, 0} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.map_pow Submodule.map_powₓ'. -/
 protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') (n : ℕ) :
     map f.toLinearMap (M ^ n) = map f.toLinearMap M ^ n :=
@@ -822,7 +818,7 @@ protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_pow Submodule.comap_unop_powₓ'. -/
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
@@ -834,7 +830,7 @@ theorem comap_unop_pow (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_pow Submodule.comap_op_powₓ'. -/
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -846,7 +842,7 @@ theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_pow Submodule.map_op_powₓ'. -/
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -858,7 +854,7 @@ theorem map_op_pow (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_pow Submodule.map_unop_powₓ'. -/
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
@@ -1131,7 +1127,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {B : Type.{u3}} [_inst_4 : CommSemiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4)] (I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (h : AlgEquiv.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (instHDiv.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.hasDiv.{u1, u3} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) J))
 but is expected to have type
-  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {B : Type.{u1}} [_inst_4 : CommSemiring.{u1} B] [_inst_5 : Algebra.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4)] (I : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (J : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (h : AlgEquiv.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (instHDiv.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (instHDiv.{u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) J))
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {B : Type.{u1}} [_inst_4 : CommSemiring.{u1} B] [_inst_5 : Algebra.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4)] (I : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (J : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (h : AlgEquiv.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (instHDiv.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (instHDiv.{u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) J))
 Case conversion may be inaccurate. Consider using '#align submodule.map_div Submodule.map_divₓ'. -/
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -722,7 +722,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5926 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5912 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5911) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -110,7 +110,7 @@ theorem one_eq_range : (1 : Submodule R A) = (Algebra.linearMap R A).range :=
 
 /- warning: submodule.le_one_to_add_submonoid -> Submodule.le_one_toAddSubmonoid is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (OfNat.mk.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.one.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toHasLe.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (OfNat.mk.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.one.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.toOfNat1.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.one.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoidₓ'. -/
@@ -163,11 +163,15 @@ theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
 -/
 
-#print Submodule.one_le /-
+/- warning: submodule.one_le -> Submodule.one_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) P) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) P)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) P) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) P)
+Case conversion may be inaccurate. Consider using '#align submodule.one_le Submodule.one_leₓ'. -/
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
   simpa only [one_eq_span, span_le, Set.singleton_subset_iff]
 #align submodule.one_le Submodule.one_le
--/
 
 /- warning: submodule.map_one -> Submodule.map_one is a dubious translation:
 lean 3 declaration is
@@ -252,7 +256,7 @@ theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
 
 /- warning: submodule.mul_le -> Submodule.mul_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) P)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) P)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) P)))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le Submodule.mul_leₓ'. -/
@@ -362,24 +366,36 @@ protected theorem mul_one : M * 1 = M :=
 
 variable {M N P Q}
 
-#print Submodule.mul_le_mul /-
+/- warning: submodule.mul_le_mul -> Submodule.mul_le_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N Q) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N Q) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul Submodule.mul_le_mulₓ'. -/
 @[mono]
 theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
   map₂_le_map₂ hmp hnq
 #align submodule.mul_le_mul Submodule.mul_le_mul
--/
 
-#print Submodule.mul_le_mul_left /-
+/- warning: submodule.mul_le_mul_left -> Submodule.mul_le_mul_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_left Submodule.mul_le_mul_leftₓ'. -/
 theorem mul_le_mul_left (h : M ≤ N) : M * P ≤ N * P :=
   map₂_le_map₂_left h
 #align submodule.mul_le_mul_left Submodule.mul_le_mul_left
--/
 
-#print Submodule.mul_le_mul_right /-
+/- warning: submodule.mul_le_mul_right -> Submodule.mul_le_mul_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) N P) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_le_mul_right Submodule.mul_le_mul_rightₓ'. -/
 theorem mul_le_mul_right (h : N ≤ P) : M * N ≤ M * P :=
   map₂_le_map₂_right h
 #align submodule.mul_le_mul_right Submodule.mul_le_mul_right
--/
 
 variable (M N P)
 
@@ -667,7 +683,7 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
 
 /- warning: submodule.le_pow_to_add_submonoid -> Submodule.le_pow_toAddSubmonoid is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toHasLe.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
 Case conversion may be inaccurate. Consider using '#align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoidₓ'. -/
@@ -1051,7 +1067,7 @@ theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔
 
 /- warning: submodule.le_div_iff -> Submodule.le_div_iff is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x z) J)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x z) J)))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x z) J)))
 Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff Submodule.le_div_iffₓ'. -/
@@ -1061,7 +1077,7 @@ theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z
 
 /- warning: submodule.le_div_iff_mul_le -> Submodule.le_div_iff_mul_le is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
 Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_leₓ'. -/
@@ -1071,7 +1087,7 @@ theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J
 
 /- warning: submodule.one_le_one_div -> Submodule.one_le_one_div is a dubious translation:
 lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))
 but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.one_le_one_div Submodule.one_le_one_divₓ'. -/
@@ -1083,16 +1099,25 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   · rwa [le_div_iff_mul_le, one_mul]
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
+/- warning: submodule.le_self_mul_one_div -> Submodule.le_self_mul_one_div is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) -> (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)))
+Case conversion may be inaccurate. Consider using '#align submodule.le_self_mul_one_div Submodule.le_self_mul_one_divₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
-#print Submodule.le_self_mul_one_div /-
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
   by
   rw [← mul_one I]
   apply mul_le_mul_right (one_le_one_div.mpr hI)
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
--/
 
-#print Submodule.mul_one_div_le_one /-
+/- warning: submodule.mul_one_div_le_one -> Submodule.mul_one_div_le_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toHasLe.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_one_div_le_one Submodule.mul_one_div_le_oneₓ'. -/
 theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
@@ -1101,7 +1126,6 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   rw [mul_comm]
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
--/
 
 /- warning: submodule.map_div -> Submodule.map_div is a dubious translation:
 lean 3 declaration is

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

@@ -419,7 +419,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
   calc
     map f.toLinearMap (M * N) = ⨆ i : M, (N.map (LinearMap.mul R A i)).map f.toLinearMap :=
-      map_supᵢ _ _
+      map_iSup _ _
     _ = map f.toLinearMap M * map f.toLinearMap N :=
       by
       apply congr_arg Sup
@@ -554,20 +554,20 @@ theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A)
   map₂_eq_span_image2 _ s t
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
 
-/- warning: submodule.supr_mul -> Submodule.supᵢ_mul is a dubious translation:
+/- warning: submodule.supr_mul -> Submodule.iSup_mul is a dubious translation:
 lean 3 declaration is
-  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
+  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
 but is expected to have type
-  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
-Case conversion may be inaccurate. Consider using '#align submodule.supr_mul Submodule.supᵢ_mulₓ'. -/
-theorem supᵢ_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
-  map₂_supᵢ_left _ s t
-#align submodule.supr_mul Submodule.supᵢ_mul
-
-#print Submodule.mul_supᵢ /-
-theorem mul_supᵢ (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
-  map₂_supᵢ_right _ t s
-#align submodule.mul_supr Submodule.mul_supᵢ
+  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (iSup.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_mul Submodule.iSup_mulₓ'. -/
+theorem iSup_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
+  map₂_iSup_left _ s t
+#align submodule.supr_mul Submodule.iSup_mul
+
+#print Submodule.mul_iSup /-
+theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
+  map₂_iSup_right _ t s
+#align submodule.mul_supr Submodule.mul_iSup
 -/
 
 /- warning: submodule.mem_span_mul_finite_of_mem_mul -> Submodule.mem_span_mul_finite_of_mem_mul is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -706,7 +706,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5950 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5926 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5925) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]

mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c

@@ -406,7 +406,7 @@ but is expected to have type
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) N)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_subset_mul Submodule.mul_subset_mulₓ'. -/
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
-  image2_subset_map₂ (LinearMap.Algebra.lmul R A).toLinearMap M N
+  image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
 /- warning: submodule.map_mul -> Submodule.map_mul is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -270,7 +270,7 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid :=
   by
   dsimp [Mul.mul]
-  simp_rw [← LinearMap.mulLeft_toAddMonoid_hom R, LinearMap.mulLeft, ← map_to_add_submonoid _ N,
+  simp_rw [← LinearMap.mulLeft_toAddMonoidHom R, LinearMap.mulLeft, ← map_to_add_submonoid _ N,
     map₂]
   rw [supr_to_add_submonoid]
   rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

@@ -186,7 +186,7 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
@@ -201,7 +201,7 @@ theorem map_op_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
@@ -215,7 +215,7 @@ theorem comap_op_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_one Submodule.map_unop_oneₓ'. -/
 @[simp]
 theorem map_unop_one :
@@ -227,7 +227,7 @@ theorem map_unop_one :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_one Submodule.comap_unop_oneₓ'. -/
 @[simp]
 theorem comap_unop_one :
@@ -442,7 +442,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_mul Submodule.map_op_mulₓ'. -/
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -464,7 +464,7 @@ theorem map_op_mul :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_mul Submodule.comap_unop_mulₓ'. -/
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -477,7 +477,7 @@ theorem comap_unop_mul :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_mul Submodule.map_unop_mulₓ'. -/
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
@@ -494,7 +494,7 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_mul Submodule.comap_op_mulₓ'. -/
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
@@ -776,7 +776,7 @@ def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.hasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (MulOpposite.hasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.instMulMulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.instAddMulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.add.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
 Case conversion may be inaccurate. Consider using '#align submodule.equiv_opposite Submodule.equivOppositeₓ'. -/
 /-- The ring of submodules of the opposite algebra is isomorphic to the opposite ring of
 submodules. -/
@@ -806,7 +806,7 @@ protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_pow Submodule.comap_unop_powₓ'. -/
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
@@ -818,7 +818,7 @@ theorem comap_unop_pow (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.comap_op_pow Submodule.comap_op_powₓ'. -/
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -830,7 +830,7 @@ theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.map_op_pow Submodule.map_op_powₓ'. -/
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
@@ -842,7 +842,7 @@ theorem map_op_pow (n : ℕ) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
 Case conversion may be inaccurate. Consider using '#align submodule.map_unop_pow Submodule.map_unop_powₓ'. -/
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

@@ -124,7 +124,7 @@ theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
@@ -134,7 +134,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
@@ -163,15 +163,11 @@ theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
 -/
 
-/- warning: submodule.one_le -> Submodule.one_le is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) P) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) P)
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) P) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) P)
-Case conversion may be inaccurate. Consider using '#align submodule.one_le Submodule.one_leₓ'. -/
+#print Submodule.one_le /-
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
   simpa only [one_eq_span, span_le, Set.singleton_subset_iff]
 #align submodule.one_le Submodule.one_le
+-/
 
 /- warning: submodule.map_one -> Submodule.map_one is a dubious translation:
 lean 3 declaration is
@@ -248,7 +244,7 @@ instance : Mul (Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul Submodule.mul_mem_mulₓ'. -/
 theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
   apply_mem_map₂ _ hm hn
@@ -258,7 +254,7 @@ theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) P)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) P)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) P)))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_le Submodule.mul_leₓ'. -/
 theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
   map₂_le
@@ -284,7 +280,7 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
 Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on Submodule.mul_induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
@@ -298,7 +294,7 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
 Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on' Submodule.mul_induction_on'ₓ'. -/
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
@@ -407,7 +403,7 @@ theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) N)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) N)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) N)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_subset_mul Submodule.mul_subset_mulₓ'. -/
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
   image2_subset_map₂ (LinearMap.Algebra.lmul R A).toLinearMap M N
@@ -532,7 +528,7 @@ open Classical
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : AddCommMonoid.{u2} A] [_inst_6 : Mul.{u2} A] [_inst_7 : Module.{u1, u2} R A _inst_4 _inst_5] {S : Set.{u2} A} {S' : Set.{u2} A} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) S S'))) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) S) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') S') (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} A] [_inst_6 : Mul.{u1} A] [_inst_7 : Module.{u2, u1} R A _inst_4 _inst_5] {S : Set.{u1} A} {S' : Set.{u1} A} {x : A}, (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.instSetLikeSubmodule.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) S S'))) -> (Exists.{succ u1} (Finset.{u1} A) (fun (T : Finset.{u1} A) => Exists.{succ u1} (Finset.{u1} A) (fun (T' : Finset.{u1} A) => And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T) S) (And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T') S') (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.instSetLikeSubmodule.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) (Finset.toSet.{u1} A T) (Finset.toSet.{u1} A T'))))))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} A] [_inst_6 : Mul.{u1} A] [_inst_7 : Module.{u2, u1} R A _inst_4 _inst_5] {S : Set.{u1} A} {S' : Set.{u1} A} {x : A}, (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) S S'))) -> (Exists.{succ u1} (Finset.{u1} A) (fun (T : Finset.{u1} A) => Exists.{succ u1} (Finset.{u1} A) (fun (T' : Finset.{u1} A) => And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T) S) (And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T') S') (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) (Finset.toSet.{u1} A T) (Finset.toSet.{u1} A T'))))))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_span_mul Submodule.mem_span_mul_finite_of_mem_span_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :
@@ -552,7 +548,7 @@ end DecidableEq
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) t)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) t)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) t)))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_setₓ'. -/
 theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A) * (t : Set A)) :=
   map₂_eq_span_image2 _ s t
@@ -578,7 +574,7 @@ theorem mul_supᵢ (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i,
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) Q)) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T') (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Q)) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Finset.toSet.{u2} A T) (Finset.toSet.{u2} A T'))))))))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T') (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Q)) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Finset.toSet.{u2} A T) (Finset.toSet.{u2} A T'))))))))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
@@ -592,7 +588,7 @@ variable {M N P}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) y z) x)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) y z) x)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) y z) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mulₓ'. -/
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x :=
   by
@@ -604,7 +600,7 @@ theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P,
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) z y) x)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) z y) x)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) z y) x)))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singletonₓ'. -/
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x :=
   by
@@ -645,21 +641,17 @@ theorem pow_eq_span_pow_set (n : ℕ) : M ^ n = span R ((M : Set A) ^ n) := by
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (Semiring.toOne.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) n) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (Semiring.toOne.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) n) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_subset_pow Submodule.pow_subset_powₓ'. -/
 theorem pow_subset_pow {n : ℕ} : (↑M : Set A) ^ n ⊆ ↑(M ^ n : Submodule R A) :=
   (pow_eq_span_pow_set M n).symm ▸ subset_span
 #align submodule.pow_subset_pow Submodule.pow_subset_pow
 
-/- warning: submodule.pow_mem_pow -> Submodule.pow_mem_pow is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x M) -> (forall (n : Nat), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) x n) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
-but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x M) -> (forall (n : Nat), Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) x n) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
-Case conversion may be inaccurate. Consider using '#align submodule.pow_mem_pow Submodule.pow_mem_powₓ'. -/
+#print Submodule.pow_mem_pow /-
 theorem pow_mem_pow {x : A} (hx : x ∈ M) (n : ℕ) : x ^ n ∈ M ^ n :=
   pow_subset_pow _ <| Set.pow_mem_pow hx _
 #align submodule.pow_mem_pow Submodule.pow_mem_pow
+-/
 
 #print Submodule.pow_toAddSubmonoid /-
 theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.toAddSubmonoid ^ n :=
@@ -691,7 +683,7 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
@@ -714,7 +706,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5950 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5950 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
@@ -741,7 +733,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
@@ -757,7 +749,7 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/
@@ -914,7 +906,7 @@ variable {M N : Submodule R A} {m n : A}
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
 Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_revₓ'. -/
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=
   mul_comm m n ▸ mul_mem_mul hm hn
@@ -1038,7 +1030,7 @@ instance : Div (Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x y) I))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x y) I))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x y) I))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_memₓ'. -/
 theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I :=
   Iff.refl _
@@ -1048,7 +1040,7 @@ theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (SMul.smul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Mul.toSMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) J)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) I))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HSMul.hSMul.{u2, u2, u2} A (Set.{u2} A) (Set.{u2} A) (instHSMul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Algebra.toSMul.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)))) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) J)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HSMul.hSMul.{u2, u2, u2} A (Set.{u2} A) (Set.{u2} A) (instHSMul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Algebra.toSMul.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)))) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) J)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subsetₓ'. -/
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
   ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by
@@ -1061,7 +1053,7 @@ theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x z) J)))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x z) J)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x z) J)))
 Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff Submodule.le_div_iffₓ'. -/
 theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z ∈ K, x * z ∈ J :=
   Iff.refl _

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -64,7 +64,7 @@ variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
@@ -74,7 +74,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
@@ -124,7 +124,7 @@ theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
@@ -134,7 +134,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
@@ -691,7 +691,7 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
@@ -714,7 +714,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5941 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5950 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5949) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
@@ -741,7 +741,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
@@ -757,7 +757,7 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -1025,7 +1025,7 @@ instance : Div (Submodule R A) :=
   ⟨fun I J =>
     { carrier := { x | ∀ y ∈ J, x * y ∈ I }
       zero_mem' := fun y hy => by
-        rw [zero_mul]
+        rw [MulZeroClass.zero_mul]
         apply Submodule.zero_mem
       add_mem' := fun a b ha hb y hy => by
         rw [add_mul]

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module algebra.algebra.operations
-! leanprover-community/mathlib commit 27b54c47c3137250a521aa64e9f1db90be5f6a26
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -22,6 +22,9 @@ import Mathbin.GroupTheory.GroupAction.SubMulAction.Pointwise
 /-!
 # Multiplication and division of submodules of an algebra.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 An interface for multiplication and division of sub-R-modules of an R-algebra A is developed.
 
 ## Main definitions

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -61,7 +61,7 @@ variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
@@ -71,7 +71,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
@@ -121,7 +121,7 @@ theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
 Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
@@ -131,7 +131,7 @@ theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
 Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
@@ -688,7 +688,7 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
@@ -711,7 +711,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5941 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5941 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
@@ -738,7 +738,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
@@ -754,7 +754,7 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
 Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -57,10 +57,22 @@ namespace SubMulAction
 
 variable {R : Type u} {A : Type v} [CommSemiring R] [Semiring A] [Algebra R A]
 
+/- warning: sub_mul_action.algebra_map_mem -> SubMulAction.algebraMap_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))
+Case conversion may be inaccurate. Consider using '#align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : SubMulAction R A) :=
   ⟨r, (algebraMap_eq_smul_one r).symm⟩
 #align sub_mul_action.algebra_map_mem SubMulAction.algebraMap_mem
 
+/- warning: sub_mul_action.mem_one' -> SubMulAction.mem_one' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SetLike.hasMem.{u2, u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) A (SubMulAction.setLike.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (OfNat.mk.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) 1 (One.one.{u2} (SubMulAction.{u1, u2} R A (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (SubMulAction.hasOne.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (SubMulAction.instSetLikeSubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (SubMulAction.{u1, u2} R A (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SubMulAction.instOneSubMulActionToSMul.{u1, u2} R A (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulActionWithZero.toMulAction.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toOne.{u2} A _inst_2))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+Case conversion may be inaccurate. Consider using '#align sub_mul_action.mem_one' SubMulAction.mem_one'ₓ'. -/
 theorem mem_one' {x : A} : x ∈ (1 : SubMulAction R A) ↔ ∃ y, algebraMap R A y = x :=
   exists_congr fun r => by rw [algebra_map_eq_smul_one]
 #align sub_mul_action.mem_one' SubMulAction.mem_one'
@@ -83,45 +95,87 @@ variable (S T : Set A) {M N P Q : Submodule R A} {m n : A}
 instance : One (Submodule R A) :=
   ⟨(Algebra.linearMap R A).range⟩
 
+/- warning: submodule.one_eq_range -> Submodule.one_eq_range is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (LinearMap.range.{u1, u1, u1, u2, max u1 u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u1, u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.linearMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (LinearMap.range.{u1, u1, u1, u2, max u1 u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u1, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) R A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u1, u2} R R R A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Algebra.linearMap.{u1, u2} R A _inst_1 _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align submodule.one_eq_range Submodule.one_eq_rangeₓ'. -/
 theorem one_eq_range : (1 : Submodule R A) = (Algebra.linearMap R A).range :=
   rfl
 #align submodule.one_eq_range Submodule.one_eq_range
 
+/- warning: submodule.le_one_to_add_submonoid -> Submodule.le_one_toAddSubmonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (OfNat.mk.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.one.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (OfNat.ofNat.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) 1 (One.toOfNat1.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.one.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoidₓ'. -/
 theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid :=
   by
   rintro x ⟨n, rfl⟩
   exact ⟨n, map_natCast (algebraMap R A) n⟩
 #align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoid
 
+/- warning: submodule.algebra_map_mem -> Submodule.algebraMap_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (r : R), Membership.mem.{u2, u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) r) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.algebra_map_mem Submodule.algebraMap_memₓ'. -/
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
   LinearMap.mem_range_self _ _
 #align submodule.algebra_map_mem Submodule.algebraMap_mem
 
+/- warning: submodule.mem_one -> Submodule.mem_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {x : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (Exists.{succ u1} R (fun (y : R) => Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) y) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) y) x))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_one Submodule.mem_oneₓ'. -/
 @[simp]
 theorem mem_one {x : A} : x ∈ (1 : Submodule R A) ↔ ∃ y, algebraMap R A y = x :=
   Iff.rfl
 #align submodule.mem_one Submodule.mem_one
 
+#print Submodule.toSubMulAction_one /-
 @[simp]
 theorem toSubMulAction_one : (1 : Submodule R A).toSubMulAction = 1 :=
   SetLike.ext fun x => mem_one.trans SubMulAction.mem_one'.symm
 #align submodule.to_sub_mul_action_one Submodule.toSubMulAction_one
+-/
 
+#print Submodule.one_eq_span /-
 theorem one_eq_span : (1 : Submodule R A) = R ∙ 1 :=
   by
   apply Submodule.ext
   intro a
   simp only [mem_one, mem_span_singleton, Algebra.smul_def, mul_one]
 #align submodule.one_eq_span Submodule.one_eq_span
+-/
 
+#print Submodule.one_eq_span_one_set /-
 theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
   one_eq_span
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
+-/
 
+/- warning: submodule.one_le -> Submodule.one_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) P) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (OfNat.mk.{u2} A 1 (One.one.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))) P)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) P) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} A 1 (One.toOfNat1.{u2} A (Semiring.toOne.{u2} A _inst_2))) P)
+Case conversion may be inaccurate. Consider using '#align submodule.one_le Submodule.one_leₓ'. -/
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
   simpa only [one_eq_span, span_le, Set.singleton_subset_iff]
 #align submodule.one_le Submodule.one_le
 
+/- warning: submodule.map_one -> Submodule.map_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (OfNat.mk.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) 1 (One.one.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u1, u3} R _inst_1 A' _inst_4 _inst_5))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (OfNat.ofNat.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u2, u3} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) 1 (One.toOfNat1.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.one.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))
+Case conversion may be inaccurate. Consider using '#align submodule.map_one Submodule.map_oneₓ'. -/
 protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (1 : Submodule R A) = 1 :=
   by
@@ -129,6 +183,12 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
   simp
 #align submodule.map_one Submodule.map_one
 
+/- warning: submodule.map_op_one -> Submodule.map_op_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align submodule.map_op_one Submodule.map_op_oneₓ'. -/
 @[simp]
 theorem map_op_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 :=
@@ -138,6 +198,12 @@ theorem map_op_one :
   simp
 #align submodule.map_op_one Submodule.map_op_one
 
+/- warning: submodule.comap_op_one -> Submodule.comap_op_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.comap_op_one Submodule.comap_op_oneₓ'. -/
 @[simp]
 theorem comap_op_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 :=
@@ -146,12 +212,24 @@ theorem comap_op_one :
   simp
 #align submodule.comap_op_one Submodule.comap_op_one
 
+/- warning: submodule.map_unop_one -> Submodule.map_unop_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.map_unop_one Submodule.map_unop_oneₓ'. -/
 @[simp]
 theorem map_unop_one :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R Aᵐᵒᵖ) = 1 := by
   rw [← comap_equiv_eq_map_symm, comap_op_one]
 #align submodule.map_unop_one Submodule.map_unop_one
 
+/- warning: submodule.comap_unop_one -> Submodule.comap_unop_one is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.one.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_one Submodule.comap_unop_oneₓ'. -/
 @[simp]
 theorem comap_unop_one :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (1 : Submodule R A) = 1 := by
@@ -163,14 +241,32 @@ smallest R-submodule of `A` containing the elements `m * n` for `m ∈ M` and `n
 instance : Mul (Submodule R A) :=
   ⟨Submodule.map₂ <| LinearMap.mul R A⟩
 
+/- warning: submodule.mul_mem_mul -> Submodule.mul_mem_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul Submodule.mul_mem_mulₓ'. -/
 theorem mul_mem_mul (hm : m ∈ M) (hn : n ∈ N) : m * n ∈ M * N :=
   apply_mem_map₂ _ hm hn
 #align submodule.mul_mem_mul Submodule.mul_mem_mul
 
+/- warning: submodule.mul_le -> Submodule.mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) P)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) P) (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) P)))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_le Submodule.mul_leₓ'. -/
 theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
   map₂_le
 #align submodule.mul_le Submodule.mul_le
 
+/- warning: submodule.mul_to_add_submonoid -> Submodule.mul_toAddSubmonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHMul.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.hasMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) N))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHMul.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.mul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) N))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoidₓ'. -/
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid :=
   by
@@ -181,6 +277,12 @@ theorem mul_toAddSubmonoid (M N : Submodule R A) :
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
 
+/- warning: submodule.mul_induction_on -> Submodule.mul_induction_on is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : A -> Prop} {r : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (n : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n)))) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (C r)
+Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on Submodule.mul_induction_onₓ'. -/
 @[elab_as_elim]
 protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
     (hm : ∀ m ∈ M, ∀ n ∈ N, C (m * n)) (ha : ∀ x y, C x → C y → C (x + y)) : C r :=
@@ -189,6 +291,12 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
   exact AddSubmonoid.mul_induction_on hr hm ha
 #align submodule.mul_induction_on Submodule.mul_induction_on
 
+/- warning: submodule.mul_induction_on' -> Submodule.mul_induction_on' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {C : forall (r : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) -> Prop}, (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (n : A) (H_1 : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) n N), C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m n) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M N m n H H_1)) -> (forall (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (y : A) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), (C x hx) -> (C y hy) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N) x y hx hy))) -> (forall {r : A} (hr : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) r (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)), C r hr)
+Case conversion may be inaccurate. Consider using '#align submodule.mul_induction_on' Submodule.mul_induction_on'ₓ'. -/
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
 protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
@@ -203,6 +311,12 @@ protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
 
 variable (R)
 
+/- warning: submodule.span_mul_span -> Submodule.span_mul_span is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} A) (T : Set.{u2} A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) S T))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (S : Set.{u2} A) (T : Set.{u2} A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) S) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) T)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) S T))
+Case conversion may be inaccurate. Consider using '#align submodule.span_mul_span Submodule.span_mul_spanₓ'. -/
 theorem span_mul_span : span R S * span R T = span R (S * T) :=
   map₂_span_span _ _ _ _
 #align submodule.span_mul_span Submodule.span_mul_span
@@ -211,59 +325,97 @@ variable {R}
 
 variable (M N P Q)
 
+#print Submodule.mul_bot /-
 @[simp]
 theorem mul_bot : M * ⊥ = ⊥ :=
   map₂_bot_right _ _
 #align submodule.mul_bot Submodule.mul_bot
+-/
 
+/- warning: submodule.bot_mul -> Submodule.bot_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasBot.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.hasBot.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instBotSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) (Bot.bot.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.instBotSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.bot_mul Submodule.bot_mulₓ'. -/
 @[simp]
 theorem bot_mul : ⊥ * M = ⊥ :=
   map₂_bot_left _ _
 #align submodule.bot_mul Submodule.bot_mul
 
+#print Submodule.one_mul /-
 @[simp]
 protected theorem one_mul : (1 : Submodule R A) * M = M :=
   by
   conv_lhs => rw [one_eq_span, ← span_eq M]
   erw [span_mul_span, one_mul, span_eq]
 #align submodule.one_mul Submodule.one_mul
+-/
 
+#print Submodule.mul_one /-
 @[simp]
 protected theorem mul_one : M * 1 = M :=
   by
   conv_lhs => rw [one_eq_span, ← span_eq M]
   erw [span_mul_span, mul_one, span_eq]
 #align submodule.mul_one Submodule.mul_one
+-/
 
 variable {M N P Q}
 
+#print Submodule.mul_le_mul /-
 @[mono]
 theorem mul_le_mul (hmp : M ≤ P) (hnq : N ≤ Q) : M * N ≤ P * Q :=
   map₂_le_map₂ hmp hnq
 #align submodule.mul_le_mul Submodule.mul_le_mul
+-/
 
+#print Submodule.mul_le_mul_left /-
 theorem mul_le_mul_left (h : M ≤ N) : M * P ≤ N * P :=
   map₂_le_map₂_left h
 #align submodule.mul_le_mul_left Submodule.mul_le_mul_left
+-/
 
+#print Submodule.mul_le_mul_right /-
 theorem mul_le_mul_right (h : N ≤ P) : M * N ≤ M * P :=
   map₂_le_map₂_right h
 #align submodule.mul_le_mul_right Submodule.mul_le_mul_right
+-/
 
 variable (M N P)
 
+#print Submodule.mul_sup /-
 theorem mul_sup : M * (N ⊔ P) = M * N ⊔ M * P :=
   map₂_sup_right _ _ _ _
 #align submodule.mul_sup Submodule.mul_sup
+-/
 
+/- warning: submodule.sup_mul -> Submodule.sup_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) P) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toHasSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) M N) P) (Sup.sup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SemilatticeSup.toSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Lattice.toSemilatticeSup.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M P) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) N P))
+Case conversion may be inaccurate. Consider using '#align submodule.sup_mul Submodule.sup_mulₓ'. -/
 theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
   map₂_sup_left _ _ _ _
 #align submodule.sup_mul Submodule.sup_mul
 
+/- warning: submodule.mul_subset_mul -> Submodule.mul_subset_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) N)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) N)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_subset_mul Submodule.mul_subset_mulₓ'. -/
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
   image2_subset_map₂ (LinearMap.Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
+/- warning: submodule.map_mul -> Submodule.map_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u3, u3, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u1, u3} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u1, u1, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHMul.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.mul.{u2, u1} R _inst_1 A' _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) N))
+Case conversion may be inaccurate. Consider using '#align submodule.map_mul Submodule.map_mulₓ'. -/
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
   calc
@@ -287,6 +439,12 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
     
 #align submodule.map_mul Submodule.map_mul
 
+/- warning: submodule.map_op_mul -> Submodule.map_op_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+Case conversion may be inaccurate. Consider using '#align submodule.map_op_mul Submodule.map_op_mulₓ'. -/
 theorem map_op_mul :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
@@ -303,6 +461,12 @@ theorem map_op_mul :
     exact mul_mem_mul hn hm
 #align submodule.map_op_mul Submodule.map_op_mul
 
+/- warning: submodule.comap_unop_mul -> Submodule.comap_unop_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_mul Submodule.comap_unop_mulₓ'. -/
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
@@ -310,6 +474,12 @@ theorem comap_unop_mul :
   by simp_rw [← map_equiv_eq_comap_symm, map_op_mul]
 #align submodule.comap_unop_mul Submodule.comap_unop_mul
 
+/- warning: submodule.map_unop_mul -> Submodule.map_unop_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) N) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M))
+Case conversion may be inaccurate. Consider using '#align submodule.map_unop_mul Submodule.map_unop_mulₓ'. -/
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
@@ -321,6 +491,12 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
       LinearEquiv.symm_trans_self, LinearEquiv.refl_toLinearMap, map_id, map_id, map_id]
 #align submodule.map_unop_mul Submodule.map_unop_mul
 
+/- warning: submodule.comap_op_mul -> Submodule.comap_op_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (N : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHMul.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M N)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) N) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M))
+Case conversion may be inaccurate. Consider using '#align submodule.comap_op_mul Submodule.comap_op_mulₓ'. -/
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
@@ -332,12 +508,14 @@ section
 
 open Pointwise
 
+#print Submodule.hasDistribPointwiseNeg /-
 /-- `submodule.has_pointwise_neg` distributes over multiplication.
 
 This is available as an instance in the `pointwise` locale. -/
 protected def hasDistribPointwiseNeg {A} [Ring A] [Algebra R A] : HasDistribNeg (Submodule R A) :=
   toAddSubmonoid_injective.HasDistribNeg _ neg_toAddSubmonoid mul_toAddSubmonoid
 #align submodule.has_distrib_pointwise_neg Submodule.hasDistribPointwiseNeg
+-/
 
 scoped[Pointwise] attribute [instance] Submodule.hasDistribPointwiseNeg
 
@@ -347,6 +525,12 @@ section DecidableEq
 
 open Classical
 
+/- warning: submodule.mem_span_mul_finite_of_mem_span_mul -> Submodule.mem_span_mul_finite_of_mem_span_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_4 : Semiring.{u1} R] [_inst_5 : AddCommMonoid.{u2} A] [_inst_6 : Mul.{u2} A] [_inst_7 : Module.{u1, u2} R A _inst_4 _inst_5] {S : Set.{u2} A} {S' : Set.{u2} A} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) S S'))) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) S) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') S') (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A _inst_4 _inst_5 _inst_7) A (Submodule.setLike.{u1, u2} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u1, u2} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A _inst_6)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_4 : Semiring.{u2} R] [_inst_5 : AddCommMonoid.{u1} A] [_inst_6 : Mul.{u1} A] [_inst_7 : Module.{u2, u1} R A _inst_4 _inst_5] {S : Set.{u1} A} {S' : Set.{u1} A} {x : A}, (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.instSetLikeSubmodule.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) S S'))) -> (Exists.{succ u1} (Finset.{u1} A) (fun (T : Finset.{u1} A) => Exists.{succ u1} (Finset.{u1} A) (fun (T' : Finset.{u1} A) => And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T) S) (And (HasSubset.Subset.{u1} (Set.{u1} A) (Set.instHasSubsetSet.{u1} A) (Finset.toSet.{u1} A T') S') (Membership.mem.{u1, u1} A (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} R A _inst_4 _inst_5 _inst_7) A (Submodule.instSetLikeSubmodule.{u2, u1} R A _inst_4 _inst_5 _inst_7)) x (Submodule.span.{u2, u1} R A _inst_4 _inst_5 _inst_7 (HMul.hMul.{u1, u1, u1} (Set.{u1} A) (Set.{u1} A) (Set.{u1} A) (instHMul.{u1} (Set.{u1} A) (Set.mul.{u1} A _inst_6)) (Finset.toSet.{u1} A T) (Finset.toSet.{u1} A T'))))))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_span_mul Submodule.mem_span_mul_finite_of_mem_span_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :
     ∃ T T' : Finset A, ↑T ⊆ S ∧ ↑T' ⊆ S' ∧ x ∈ span R (T * T' : Set A) :=
@@ -361,18 +545,38 @@ theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A]
 
 end DecidableEq
 
+/- warning: submodule.mul_eq_span_mul_set -> Submodule.mul_eq_span_mul_set is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) s) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) t)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (s : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (t : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) s t) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) s) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) t)))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_setₓ'. -/
 theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A) * (t : Set A)) :=
   map₂_eq_span_image2 _ s t
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
 
+/- warning: submodule.supr_mul -> Submodule.supᵢ_mul is a dubious translation:
+lean 3 declaration is
+  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toHasSup.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
+but is expected to have type
+  forall {ι : Sort.{u1}} {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (s : ι -> (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3))) (t : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => s i)) t) (supᵢ.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.completeLattice.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)))) ι (fun (i : ι) => HMul.hMul.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u2, u3} R _inst_1 A _inst_2 _inst_3)) (s i) t))
+Case conversion may be inaccurate. Consider using '#align submodule.supr_mul Submodule.supᵢ_mulₓ'. -/
 theorem supᵢ_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
   map₂_supᵢ_left _ s t
 #align submodule.supr_mul Submodule.supᵢ_mul
 
+#print Submodule.mul_supᵢ /-
 theorem mul_supᵢ (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
   map₂_supᵢ_right _ t s
 #align submodule.mul_supr Submodule.mul_supᵢ
+-/
 
+/- warning: submodule.mem_span_mul_finite_of_mem_mul -> Submodule.mem_span_mul_finite_of_mem_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T') ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) Q)) (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} A) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} A) (Set.{u2} A) (Finset.Set.hasCoeT.{u2} A))) T'))))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {Q : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P Q)) -> (Exists.{succ u2} (Finset.{u2} A) (fun (T : Finset.{u2} A) => Exists.{succ u2} (Finset.{u2} A) (fun (T' : Finset.{u2} A) => And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) P)) (And (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (Finset.toSet.{u2} A T') (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Q)) (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HMul.hMul.{u2, u2, u2} (Set.{u2} A) (Set.{u2} A) (Set.{u2} A) (instHMul.{u2} (Set.{u2} A) (Set.mul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Finset.toSet.{u2} A T) (Finset.toSet.{u2} A T'))))))))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_span_mul_finite_of_mem_mul Submodule.mem_span_mul_finite_of_mem_mulₓ'. -/
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=
   Submodule.mem_span_mul_finite_of_mem_span_mul
@@ -381,12 +585,24 @@ theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈
 
 variable {M N P}
 
+/- warning: submodule.mem_span_singleton_mul -> Submodule.mem_span_singleton_mul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) y z) x)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)) P)) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) y z) x)))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mulₓ'. -/
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x :=
   by
   simp_rw [(· * ·), map₂_span_singleton_eq_map, exists_prop]
   rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
 
+/- warning: submodule.mem_mul_span_singleton -> Submodule.mem_mul_span_singleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => Exists.{0} (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (fun (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) => Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) z y) x)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {P : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)} {x : A} {y : A}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) P (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.instSingletonSet.{u2} A) y)))) (Exists.{succ u2} A (fun (z : A) => And (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) z P) (Eq.{succ u2} A (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) z y) x)))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singletonₓ'. -/
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x :=
   by
   simp_rw [(· * ·), map₂_span_singleton_eq_map_flip, exists_prop]
@@ -396,7 +612,7 @@ theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P,
 /-- Sub-R-modules of an R-algebra form an idempotent semiring. -/
 instance : IdemSemiring (Submodule R A) :=
   { toAddSubmonoid_injective.Semigroup _ fun m n : Submodule R A => mul_toAddSubmonoid m n,
-    AddMonoidWithOne.unary, Submodule.pointwiseAddCommMonoid, Submodule.hasOne, Submodule.hasMul,
+    AddMonoidWithOne.unary, Submodule.pointwiseAddCommMonoid, Submodule.one, Submodule.mul,
     (by infer_instance : OrderBot (Submodule R A)),
     (by infer_instance :
       Lattice (Submodule R A)) with
@@ -409,23 +625,40 @@ instance : IdemSemiring (Submodule R A) :=
 
 variable (M)
 
+#print Submodule.span_pow /-
 theorem span_pow (s : Set A) : ∀ n : ℕ, span R s ^ n = span R (s ^ n)
   | 0 => by rw [pow_zero, pow_zero, one_eq_span_one_set]
   | n + 1 => by rw [pow_succ, pow_succ, span_pow, span_mul_span]
 #align submodule.span_pow Submodule.span_pow
+-/
 
+#print Submodule.pow_eq_span_pow_set /-
 theorem pow_eq_span_pow_set (n : ℕ) : M ^ n = span R ((M : Set A) ^ n) := by
   rw [← span_pow, span_eq]
 #align submodule.pow_eq_span_pow_set Submodule.pow_eq_span_pow_set
+-/
 
+/- warning: submodule.pow_subset_pow -> Submodule.pow_subset_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (AddMonoidWithOne.toOne.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) M) n) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HPow.hPow.{u2, 0, u2} (Set.{u2} A) Nat (Set.{u2} A) (instHPow.{u2, 0} (Set.{u2} A) Nat (Set.NPow.{u2} A (Semiring.toOne.{u2} A _inst_2) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) M) n) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+Case conversion may be inaccurate. Consider using '#align submodule.pow_subset_pow Submodule.pow_subset_powₓ'. -/
 theorem pow_subset_pow {n : ℕ} : (↑M : Set A) ^ n ⊆ ↑(M ^ n : Submodule R A) :=
   (pow_eq_span_pow_set M n).symm ▸ subset_span
 #align submodule.pow_subset_pow Submodule.pow_subset_pow
 
+/- warning: submodule.pow_mem_pow -> Submodule.pow_mem_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {x : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x M) -> (forall (n : Nat), Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) x n) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {x : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x M) -> (forall (n : Nat), Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} A Nat A (instHPow.{u2, 0} A Nat (Monoid.Pow.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)))) x n) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+Case conversion may be inaccurate. Consider using '#align submodule.pow_mem_pow Submodule.pow_mem_powₓ'. -/
 theorem pow_mem_pow {x : A} (hx : x ∈ M) (n : ℕ) : x ^ n ∈ M ^ n :=
   pow_subset_pow _ <| Set.pow_mem_pow hx _
 #align submodule.pow_mem_pow Submodule.pow_mem_pow
 
+#print Submodule.pow_toAddSubmonoid /-
 theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.toAddSubmonoid ^ n :=
   by
   induction' n with n ih
@@ -435,7 +668,14 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
     · rw [pow_zero, pow_zero, mul_one, ← mul_to_add_submonoid, mul_one]
     · rw [ih n.succ_ne_zero]
 #align submodule.pow_to_add_submonoid Submodule.pow_toAddSubmonoid
+-/
 
+/- warning: submodule.le_pow_to_add_submonoid -> Submodule.le_pow_toAddSubmonoid is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteSemilatticeInf.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.toCompleteSemilatticeInf.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.completeLattice.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {n : Nat}, LE.le.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Preorder.toLE.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (PartialOrder.toPreorder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (OmegaCompletePartialOrder.toPartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.instCompleteLatticeAddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))))))) (HPow.hPow.{u2, 0, u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (instHPow.{u2, 0} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) Nat (Monoid.Pow.{u2} (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (AddSubmonoid.monoid.{u2} A _inst_2))) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) M) n) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n))
+Case conversion may be inaccurate. Consider using '#align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoidₓ'. -/
 theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAddSubmonoid :=
   by
   obtain rfl | hn := Decidable.eq_or_ne n 0
@@ -444,6 +684,12 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
   · exact (pow_to_add_submonoid M hn).ge
 #align submodule.le_pow_to_add_submonoid Submodule.le_pow_toAddSubmonoid
 
+/- warning: submodule.pow_induction_on_left' -> Submodule.pow_induction_on_left' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.mul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.IdemSemiring._proof_7.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.IdemSemiring._proof_8.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Submodule.one_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (Submodule.mul_one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 M (npowRec.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.toOne.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddMonoidWithOne.unary.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddCommMonoid.toAddMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.one.{u1, u2} R _inst_1 A _inst_2 _inst_3))) (Semigroup.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) ((NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)).0) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Function.Injective.semigroup.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoid.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3) (AddSubmonoid.semigroup.{u2} A (Semiring.toNonUnitalSemiring.{u2} A _inst_2)) (Submodule.toAddSubmonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.proof_1.{u2, u1} R _inst_1 A _inst_2 _inst_3) (Submodule.idemSemiring.proof_2.{u1, u2} R _inst_1 A _inst_2 _inst_3))) i M) m x H hx))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -461,6 +707,12 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'
 
+/- warning: submodule.pow_induction_on_right' -> Submodule.pow_induction_on_right' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.to_addMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) (Eq.subst.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (fun (_x : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) => Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m) _x) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toHasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i)) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H)))) -> (forall {x : A} {n : Nat} (hx : Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : forall (n : Nat) (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> Prop}, (forall (r : R), C (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r) (Submodule.algebraMap_mem.{u1, u2} R _inst_1 A _inst_2 _inst_3 r)) -> (forall (x : A) (y : A) (i : Nat) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)) (hy : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) y (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (C i y hy) -> (C i (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y) (AddMemClass.add_mem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (AddSubmonoidClass.toAddMemClass.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.addSubmonoidClass.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) x y hx hy))) -> (forall (i : Nat) (x : A) (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i)), (C i x hx) -> (forall (m : A) (H : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M), C (Nat.succ i) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) (Eq.rec.{0, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (fun (x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940 : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (h._@.Mathlib.Algebra.Algebra.Operations._hyg.5941 : Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) => Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m) x._@.Mathlib.Algebra.Algebra.Operations._hyg.5940) (Submodule.mul_mem_mul.{u1, u2} R _inst_1 A _inst_2 _inst_3 (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M x m hx H) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Eq.symm.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOneClass.toMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Monoid.toMulOneClass.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))))))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M i) M) (pow_succ'.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))) M i))))) -> (forall {x : A} {n : Nat} (hx : Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)), C n x hx)
+Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'ₓ'. -/
 /-- Dependent version of `submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
@@ -482,6 +734,12 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
       (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'
 
+/- warning: submodule.pow_induction_on_left -> Submodule.pow_induction_on_left is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (forall (x : A), (C x) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) m x)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_left Submodule.pow_induction_on_leftₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -492,6 +750,12 @@ protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (alg
     (fun m hm i x hx => hmul _ hm _) hx
 #align submodule.pow_induction_on_left Submodule.pow_induction_on_left
 
+/- warning: submodule.pow_induction_on_right -> Submodule.pow_induction_on_right is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (fun (_x : RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) => R -> A) (RingHom.hasCoeToFun.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toHasAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {C : A -> Prop}, (forall (r : R), C (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : R) => A) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u1, u2} (RingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2)) R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2) (RingHom.instRingHomClassRingHom.{u1, u2} R A (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (algebraMap.{u1, u2} R A _inst_1 _inst_2 _inst_3) r)) -> (forall (x : A) (y : A), (C x) -> (C y) -> (C (HAdd.hAdd.{u2, u2, u2} A A A (instHAdd.{u2} A (Distrib.toAdd.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) x y))) -> (forall (x : A), (C x) -> (forall (m : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) m M) -> (C (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) x m)))) -> (forall {x : A} {n : Nat}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) x (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) -> (C x))
+Case conversion may be inaccurate. Consider using '#align submodule.pow_induction_on_right Submodule.pow_induction_on_rightₓ'. -/
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,
 is closed under addition, and holds for `x * m` where `m ∈ M` and it holds for `x` -/
 @[elab_as_elim]
@@ -501,6 +765,7 @@ protected theorem pow_induction_on_right {C : A → Prop} (hr : ∀ r : R, C (al
   Submodule.pow_induction_on_right' M hr (fun x y i hx hy => hadd x y) (fun i x hx => hmul _) hx
 #align submodule.pow_induction_on_right Submodule.pow_induction_on_right
 
+#print Submodule.mapHom /-
 /-- `submonoid.map` as a `monoid_with_zero_hom`, when applied to `alg_hom`s. -/
 @[simps]
 def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R A →*₀ Submodule R A'
@@ -510,7 +775,14 @@ def mapHom {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') : Submodule R
   map_one' := Submodule.map_one _
   map_mul' _ _ := Submodule.map_mul _ _ _
 #align submodule.map_hom Submodule.mapHom
+-/
 
+/- warning: submodule.equiv_opposite -> Submodule.equivOpposite is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.hasMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (MulOpposite.hasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toHasAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingEquiv.{u2, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.mul.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.instMulMulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (MulOpposite.instAddMulOpposite.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Distrib.toAdd.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonUnitalNonAssocSemiring.toDistrib.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))))
+Case conversion may be inaccurate. Consider using '#align submodule.equiv_opposite Submodule.equivOppositeₓ'. -/
 /-- The ring of submodules of the opposite algebra is isomorphic to the opposite ring of
 submodules. -/
 @[simps apply symm_apply]
@@ -524,35 +796,71 @@ def equivOpposite : Submodule R Aᵐᵒᵖ ≃+* (Submodule R A)ᵐᵒᵖ
   map_mul' p q := congr_arg op <| comap_op_mul _ _
 #align submodule.equiv_opposite Submodule.equivOpposite
 
+/- warning: submodule.map_pow -> Submodule.map_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u3}} [_inst_4 : Semiring.{u3} A'] [_inst_5 : Algebra.{u1, u3} R A' _inst_1 _inst_4] (f : AlgHom.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u3, 0, u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u3, 0} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u3} (Submodule.{u1, u3} R A' (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u1, u3} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A A' (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A' (Semiring.toNonAssocSemiring.{u3} A' _inst_4))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u1, u3} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgHom.toLinearMap.{u1, u2, u3} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : Semiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 _inst_2] (M : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) {A' : Type.{u1}} [_inst_4 : Semiring.{u1} A'] [_inst_5 : Algebra.{u2, u1} R A' _inst_1 _inst_4] (f : AlgHom.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5) (n : Nat), Eq.{succ u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) (HPow.hPow.{u3, 0, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u3, 0} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u2, u3} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u1, 0, u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (instHPow.{u1, 0} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) Nat (Monoid.Pow.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (MonoidWithZero.toMonoid.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Semiring.toMonoidWithZero.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (IdemSemiring.toSemiring.{u1} (Submodule.{u2, u1} R A' (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (Submodule.idemSemiring.{u2, u1} R _inst_1 A' _inst_4 _inst_5)))))) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A A' (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A A' (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A _inst_2))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A' (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A' (Semiring.toNonAssocSemiring.{u1} A' _inst_4))) (Algebra.toModule.{u2, u3} R A _inst_1 _inst_2 _inst_3) (Algebra.toModule.{u2, u1} R A' _inst_1 _inst_4 _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgHom.toLinearMap.{u2, u3, u1} R A A' _inst_1 _inst_2 _inst_4 _inst_3 _inst_5 f) M) n)
+Case conversion may be inaccurate. Consider using '#align submodule.map_pow Submodule.map_powₓ'. -/
 protected theorem map_pow {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') (n : ℕ) :
     map f.toLinearMap (M ^ n) = map f.toLinearMap M ^ n :=
   map_pow (mapHom f) M n
 #align submodule.map_pow Submodule.map_pow
 
+/- warning: submodule.comap_unop_pow -> Submodule.comap_unop_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+Case conversion may be inaccurate. Consider using '#align submodule.comap_unop_pow Submodule.comap_unop_powₓ'. -/
 theorem comap_unop_pow (n : ℕ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).symm.map_pow (op M) n
 #align submodule.comap_unop_pow Submodule.comap_unop_pow
 
+/- warning: submodule.comap_op_pow -> Submodule.comap_op_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.comap.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+Case conversion may be inaccurate. Consider using '#align submodule.comap_op_pow Submodule.comap_op_powₓ'. -/
 theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   op_injective <| (equivOpposite : Submodule R Aᵐᵒᵖ ≃+* _).map_pow M n
 #align submodule.comap_op_pow Submodule.comap_op_pow
 
+/- warning: submodule.map_op_pow -> Submodule.map_op_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (n : Nat), Eq.{succ u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) (Submodule.map.{u1, u1, u2, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A (MulOpposite.{u2} A) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) M) n)
+Case conversion may be inaccurate. Consider using '#align submodule.map_op_pow Submodule.map_op_powₓ'. -/
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
   by rw [map_equiv_eq_comap_symm, map_equiv_eq_comap_symm, comap_unop_pow]
 #align submodule.map_op_pow Submodule.map_op_pow
 
+/- warning: submodule.map_unop_pow -> Submodule.map_unop_pow is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.semiring.{u2} A _inst_2) (MulOpposite.algebra.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.semilinearMapClass.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (HasLiftT.mk.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (CoeTCₓ.coe.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (coeBase.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearEquiv.LinearMap.hasCoe.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.addCommMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] (n : Nat) (M : Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (instHPow.{u2, 0} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3))) (Submodule.idemSemiring.{u1, u2} R _inst_1 (MulOpposite.{u2} A) (MulOpposite.instSemiringMulOpposite.{u2} A _inst_2) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, u2} R A _inst_1 _inst_2 _inst_3))))))) M n)) (HPow.hPow.{u2, 0, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (instHPow.{u2, 0} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) Nat (Monoid.Pow.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (MonoidWithZero.toMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Semiring.toMonoidWithZero.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))))) (Submodule.map.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (LinearMap.instSemilinearMapClassLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} A) A (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.{u2} A) A (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (LinearEquiv.symm.{u1, u1, u2, u2} R R A (MulOpposite.{u2} A) (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (MulOpposite.instAddCommMonoidMulOpposite.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3) (MulOpposite.module.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))) M) n)
+Case conversion may be inaccurate. Consider using '#align submodule.map_unop_pow Submodule.map_unop_powₓ'. -/
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
       map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
   by rw [← comap_equiv_eq_map_symm, ← comap_equiv_eq_map_symm, comap_op_pow]
 #align submodule.map_unop_pow Submodule.map_unop_pow
 
+/- warning: submodule.span.ring_hom -> Submodule.span.ringHom is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingHom.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetSemiring.nonAssocSemiring.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2], RingHom.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (SetSemiring.instNonAssocSemiringSetSemiring.{u2} A (MulZeroOneClass.toMulOneClass.{u2} A (NonAssocSemiring.toMulZeroOneClass.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (Semiring.toNonAssocSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align submodule.span.ring_hom Submodule.span.ringHomₓ'. -/
 /-- `span` is a semiring homomorphism (recall multiplication is pointwise multiplication of subsets
 on either side). -/
 @[simps]
@@ -569,6 +877,12 @@ section
 
 variable {α : Type _} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A]
 
+/- warning: submodule.pointwise_mul_semiring_action -> Submodule.pointwiseMulSemiringAction is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} [_inst_4 : Monoid.{u3} α] [_inst_5 : MulSemiringAction.{u3, u2} α A _inst_4 _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} α R A (SMulZeroClass.toHasSmul.{u3, u2} α A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (DistribSMul.toSmulZeroClass.{u3, u2} α A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} α A _inst_4 (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} α A _inst_4 _inst_2 _inst_5)))) (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)))))], MulSemiringAction.{u3, u2} α (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_4 (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {α : Type.{u3}} [_inst_4 : Monoid.{u3} α] [_inst_5 : MulSemiringAction.{u3, u2} α A _inst_4 _inst_2] [_inst_6 : SMulCommClass.{u3, u1, u2} α R A (SMulZeroClass.toSMul.{u3, u2} α A (MonoidWithZero.toZero.{u2} A (Semiring.toMonoidWithZero.{u2} A _inst_2)) (DistribSMul.toSMulZeroClass.{u3, u2} α A (AddMonoid.toAddZeroClass.{u2} A (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))) (DistribMulAction.toDistribSMul.{u3, u2} α A _inst_4 (AddMonoidWithOne.toAddMonoid.{u2} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u2} A (NonAssocSemiring.toAddCommMonoidWithOne.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2)))) (MulSemiringAction.toDistribMulAction.{u3, u2} α A _inst_4 _inst_2 _inst_5)))) (Algebra.toSMul.{u1, u2} R A _inst_1 _inst_2 _inst_3)], MulSemiringAction.{u3, u2} α (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) _inst_4 (IdemSemiring.toSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))) (Algebra.toModule.{u1, u2} R A _inst_1 _inst_2 _inst_3)) (Submodule.idemSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))
+Case conversion may be inaccurate. Consider using '#align submodule.pointwise_mul_semiring_action Submodule.pointwiseMulSemiringActionₓ'. -/
 /-- The action on a submodule corresponding to applying the action to every element.
 
 This is available as an instance in the `pointwise` locale.
@@ -593,21 +907,35 @@ variable {A : Type v} [CommSemiring A] [Algebra R A]
 
 variable {M N : Submodule R A} {m n : A}
 
+/- warning: submodule.mul_mem_mul_rev -> Submodule.mul_mem_mul_rev is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {M : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {N : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {m : A} {n : A}, (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) m M) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) n N) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) n m) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) M N))
+Case conversion may be inaccurate. Consider using '#align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_revₓ'. -/
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=
   mul_comm m n ▸ mul_mem_mul hm hn
 #align submodule.mul_mem_mul_rev Submodule.mul_mem_mul_rev
 
 variable (M N)
 
+#print Submodule.mul_comm /-
 protected theorem mul_comm : M * N = N * M :=
   le_antisymm (mul_le.2 fun r hrm s hsn => mul_mem_mul_rev hsn hrm)
     (mul_le.2 fun r hrn s hsm => mul_mem_mul_rev hsm hrn)
 #align submodule.mul_comm Submodule.mul_comm
+-/
 
 /-- Sub-R-modules of an R-algebra A form a semiring. -/
 instance : IdemCommSemiring (Submodule R A) :=
   { Submodule.idemSemiring with mul_comm := Submodule.mul_comm }
 
+/- warning: submodule.prod_span -> Submodule.prod_span is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (M : ι -> (Set.{u2} A)), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Finset.prod.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.idemCommSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (M i))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Finset.prod.{u2, u3} (Set.{u2} A) ι (Set.commMonoid.{u2} A (CommSemiring.toCommMonoid.{u2} A _inst_2)) s (fun (i : ι) => M i)))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (M : ι -> (Set.{u3} A)), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Finset.prod.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (M i))) (Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Finset.prod.{u3, u1} (Set.{u3} A) ι (Set.commMonoid.{u3} A (CommSemiring.toCommMonoid.{u3} A _inst_2)) s (fun (i : ι) => M i)))
+Case conversion may be inaccurate. Consider using '#align submodule.prod_span Submodule.prod_spanₓ'. -/
 theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     (∏ i in s, Submodule.span R (M i)) = Submodule.span R (∏ i in s, M i) :=
   by
@@ -618,6 +946,12 @@ theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     rw [Finset.prod_insert H, Finset.prod_insert H, ih, span_mul_span]
 #align submodule.prod_span Submodule.prod_span
 
+/- warning: submodule.prod_span_singleton -> Submodule.prod_span_singleton is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {ι : Type.{u3}} (s : Finset.{u3} ι) (x : ι -> A), Eq.{succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Finset.prod.{u2, u3} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.idemCommSemiring.{u1, u2} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (x i)))) (Submodule.span.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Singleton.singleton.{u2, u2} A (Set.{u2} A) (Set.hasSingleton.{u2} A) (Finset.prod.{u2, u3} A ι (CommSemiring.toCommMonoid.{u2} A _inst_2) s (fun (i : ι) => x i))))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {ι : Type.{u1}} (s : Finset.{u1} ι) (x : ι -> A), Eq.{succ u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Finset.prod.{u3, u1} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) ι (CommSemiring.toCommMonoid.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (IdemCommSemiring.toCommSemiring.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instIdemCommSemiringSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3))) s (fun (i : ι) => Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.instSingletonSet.{u3} A) (x i)))) (Submodule.span.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Singleton.singleton.{u3, u3} A (Set.{u3} A) (Set.instSingletonSet.{u3} A) (Finset.prod.{u3, u1} A ι (CommSemiring.toCommMonoid.{u3} A _inst_2) s (fun (i : ι) => x i))))
+Case conversion may be inaccurate. Consider using '#align submodule.prod_span_singleton Submodule.prod_span_singletonₓ'. -/
 theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
     (∏ i in s, span R ({x i} : Set A)) = span R {∏ i in s, x i} := by
   rw [prod_span, Set.finset_prod_singleton]
@@ -625,6 +959,12 @@ theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
 
 variable (R A)
 
+/- warning: submodule.module_set -> Submodule.moduleSet is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Module.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemSemiring.toSemiring.{u2} (SetSemiring.{u2} A) (SetSemiring.idemSemiring.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : CommSemiring.{u1} R] (A : Type.{u2}) [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)], Module.{u2, u2} (SetSemiring.{u2} A) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (IdemSemiring.toSemiring.{u2} (SetSemiring.{u2} A) (SetSemiring.instIdemSemiringSetSemiring.{u2} A (MonoidWithZero.toMonoid.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) (Submodule.pointwiseAddCommMonoid.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))
+Case conversion may be inaccurate. Consider using '#align submodule.module_set Submodule.moduleSetₓ'. -/
 /-- R-submodules of the R-algebra A are a module over `set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A)
     where
@@ -639,15 +979,20 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A)
 
 variable {R A}
 
+#print Submodule.smul_def /-
 theorem smul_def (s : SetSemiring A) (P : Submodule R A) : s • P = span R s.down * P :=
   rfl
 #align submodule.smul_def Submodule.smul_def
+-/
 
+#print Submodule.smul_le_smul /-
 theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A} (h₁ : s.down ⊆ t.down)
     (h₂ : M ≤ N) : s • M ≤ t • N :=
   mul_le_mul (span_mono h₁) h₂
 #align submodule.smul_le_smul Submodule.smul_le_smul
+-/
 
+#print Submodule.smul_singleton /-
 theorem smul_singleton (a : A) (M : Submodule R A) :
     ({a} : Set A).up • M = M.map (LinearMap.mulLeft R a) :=
   by
@@ -662,6 +1007,7 @@ theorem smul_singleton (a : A) (M : Submodule R A) :
   · rintro _ ⟨m, hm, rfl⟩
     exact subset_span ⟨a, m, Set.mem_singleton a, hm, rfl⟩
 #align submodule.smul_singleton Submodule.smul_singleton
+-/
 
 section Quotient
 
@@ -685,10 +1031,22 @@ instance : Div (Submodule R A) :=
         rw [Algebra.smul_mul_assoc]
         exact Submodule.smul_mem _ _ (hx _ hy) }⟩
 
+/- warning: submodule.mem_div_iff_forall_mul_mem -> Submodule.mem_div_iff_forall_mul_mem is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x y) I))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (forall (y : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) y J) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x y) I))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_memₓ'. -/
 theorem mem_div_iff_forall_mul_mem {x : A} {I J : Submodule R A} : x ∈ I / J ↔ ∀ y ∈ J, x * y ∈ I :=
   Iff.refl _
 #align submodule.mem_div_iff_forall_mul_mem Submodule.mem_div_iff_forall_mul_mem
 
+/- warning: submodule.mem_div_iff_smul_subset -> Submodule.mem_div_iff_smul_subset is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.hasSubset.{u2} A) (SMul.smul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Mul.toSMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))))) x ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) J)) ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (HasLiftT.mk.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (CoeTCₓ.coe.{succ u2, succ u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Set.{u2} A) (SetLike.Set.hasCoeT.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))) I))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {x : A} {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HasSubset.Subset.{u2} (Set.{u2} A) (Set.instHasSubsetSet.{u2} A) (HSMul.hSMul.{u2, u2, u2} A (Set.{u2} A) (Set.{u2} A) (instHSMul.{u2, u2} A (Set.{u2} A) (Set.smulSet.{u2, u2} A A (Algebra.toSMul.{u2, u2} A A _inst_2 (CommSemiring.toSemiring.{u2} A _inst_2) (Algebra.id.{u2} A _inst_2)))) x (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) J)) (SetLike.coe.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I))
+Case conversion may be inaccurate. Consider using '#align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subsetₓ'. -/
 theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔ x • (J : Set A) ⊆ I :=
   ⟨fun h y ⟨y', hy', xy'_eq_y⟩ => by
     rw [← xy'_eq_y]
@@ -696,14 +1054,32 @@ theorem mem_div_iff_smul_subset {x : A} {I J : Submodule R A} : x ∈ I / J ↔
     assumption, fun h y hy => h (Set.smul_mem_smul_set hy)⟩
 #align submodule.mem_div_iff_smul_subset Submodule.mem_div_iff_smul_subset
 
+/- warning: submodule.le_div_iff -> Submodule.le_div_iff is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.Mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.setLike.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (Distrib.toHasMul.{u2} A (NonUnitalNonAssocSemiring.toDistrib.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))))) x z) J)))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (forall (x : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) x I) -> (forall (z : A), (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) z K) -> (Membership.mem.{u2, u2} A (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (SetLike.instMembership.{u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) A (Submodule.instSetLikeSubmodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HMul.hMul.{u2, u2, u2} A A A (instHMul.{u2} A (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2))))) x z) J)))
+Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff Submodule.le_div_iffₓ'. -/
 theorem le_div_iff {I J K : Submodule R A} : I ≤ J / K ↔ ∀ x ∈ I, ∀ z ∈ K, x * z ∈ J :=
   Iff.refl _
 #align submodule.le_div_iff Submodule.le_div_iff
 
+/- warning: submodule.le_div_iff_mul_le -> Submodule.le_div_iff_mul_le is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)} {K : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) J K)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (HMul.hMul.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHMul.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.mul.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) I K) J)
+Case conversion may be inaccurate. Consider using '#align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_leₓ'. -/
 theorem le_div_iff_mul_le {I J K : Submodule R A} : I ≤ J / K ↔ I * K ≤ J := by
   rw [le_div_iff, mul_le]
 #align submodule.le_div_iff_mul_le Submodule.le_div_iff_mul_le
 
+/- warning: submodule.one_le_one_div -> Submodule.one_le_one_div is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteSemilatticeInf.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (OfNat.mk.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.one.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)}, Iff (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u1, u2} R _inst_1 A _inst_2 _inst_3)) (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))) I)) (LE.le.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Preorder.toLE.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (PartialOrder.toPreorder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.completeLattice.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)))))) I (OfNat.ofNat.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) 1 (One.toOfNat1.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.one.{u1, u2} R _inst_1 A (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3))))
+Case conversion may be inaccurate. Consider using '#align submodule.one_le_one_div Submodule.one_le_one_divₓ'. -/
 @[simp]
 theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
   by
@@ -713,12 +1089,15 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 :=
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
 /- ./././Mathport/Syntax/Translate/Tactic/Lean3.lean:132:4: warning: unsupported: rw with cfg: { occs := occurrences.pos[occurrences.pos] «expr[ ,]»([1]) } -/
+#print Submodule.le_self_mul_one_div /-
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) :=
   by
   rw [← mul_one I]
   apply mul_le_mul_right (one_le_one_div.mpr hI)
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
+-/
 
+#print Submodule.mul_one_div_le_one /-
 theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   by
   rw [Submodule.mul_le]
@@ -727,7 +1106,14 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 :=
   rw [mul_comm]
   exact hn m hm
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
+-/
 
+/- warning: submodule.map_div -> Submodule.map_div is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {A : Type.{u2}} [_inst_2 : CommSemiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2)] {B : Type.{u3}} [_inst_4 : CommSemiring.{u3} B] [_inst_5 : Algebra.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4)] (I : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (J : Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (h : AlgEquiv.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5), Eq.{succ u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u2, u2, u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (instHDiv.{u2} (Submodule.{u1, u2} R A (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3)) (Submodule.hasDiv.{u1, u2} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (instHDiv.{u3} (Submodule.{u1, u3} R B (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (Submodule.hasDiv.{u1, u3} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u1, u1, u2, u3, max u2 u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (RingHomSurjective.ids.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u3} R R (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5)) (LinearMap.semilinearMapClass.{u1, u1, u2, u3} R R A B (CommSemiring.toSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B _inst_4)))) (Algebra.toModule.{u1, u2} R A _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) _inst_3) (Algebra.toModule.{u1, u3} R B _inst_1 (CommSemiring.toSemiring.{u3} B _inst_4) _inst_5) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)))) (AlgEquiv.toLinearMap.{u1, u2, u3} R A B _inst_1 (CommSemiring.toSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B _inst_4) _inst_3 _inst_5 h) J))
+but is expected to have type
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {A : Type.{u3}} [_inst_2 : CommSemiring.{u3} A] [_inst_3 : Algebra.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2)] {B : Type.{u1}} [_inst_4 : CommSemiring.{u1} B] [_inst_5 : Algebra.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4)] (I : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (J : Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (h : AlgEquiv.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5), Eq.{succ u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) (HDiv.hDiv.{u3, u3, u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (instHDiv.{u3} (Submodule.{u2, u3} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u3} R _inst_1 A _inst_2 _inst_3)) I J)) (HDiv.hDiv.{u1, u1, u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (instHDiv.{u1} (Submodule.{u2, u1} R B (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (Submodule.instDivSubmoduleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToModule.{u2, u1} R _inst_1 B _inst_4 _inst_5)) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) I) (Submodule.map.{u2, u2, u3, u1, max u3 u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (RingHomSurjective.ids.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (LinearMap.{u2, u2, u3, u1} R R (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) A B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5)) (LinearMap.instSemilinearMapClassLinearMap.{u2, u2, u3, u1} R R A B (CommSemiring.toSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} A (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A _inst_2)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B _inst_4)))) (Algebra.toModule.{u2, u3} R A _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) _inst_3) (Algebra.toModule.{u2, u1} R B _inst_1 (CommSemiring.toSemiring.{u1} B _inst_4) _inst_5) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (AlgEquiv.toLinearMap.{u2, u3, u1} R A B _inst_1 (CommSemiring.toSemiring.{u3} A _inst_2) (CommSemiring.toSemiring.{u1} B _inst_4) _inst_3 _inst_5 h) J))
+Case conversion may be inaccurate. Consider using '#align submodule.map_div Submodule.map_divₓ'. -/
 @[simp]
 protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)
     (h : A ≃ₐ[R] B) : (I / J).map h.toLinearMap = I.map h.toLinearMap / J.map h.toLinearMap :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
 
 ! This file was ported from Lean 3 source module algebra.algebra.operations
-! leanprover-community/mathlib commit 2bbc7e3884ba234309d2a43b19144105a753292e
+! leanprover-community/mathlib commit 27b54c47c3137250a521aa64e9f1db90be5f6a26
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -555,13 +555,14 @@ theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 
 /-- `span` is a semiring homomorphism (recall multiplication is pointwise multiplication of subsets
 on either side). -/
+@[simps]
 def span.ringHom : SetSemiring A →+* Submodule R A
     where
-  toFun := Submodule.span R
+  toFun s := Submodule.span R s.down
   map_zero' := span_empty
   map_one' := one_eq_span.symm
   map_add' := span_union
-  map_mul' s t := by erw [span_mul_span, ← image_mul_prod]
+  map_mul' s t := by rw [SetSemiring.down_mul, span_mul_span, ← image_mul_prod]
 #align submodule.span.ring_hom Submodule.span.ringHom
 
 section
@@ -627,25 +628,22 @@ variable (R A)
 /-- R-submodules of the R-algebra A are a module over `set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A)
     where
-  smul s P := span R s * P
+  smul s P := span R s.down * P
   smul_add _ _ _ := mul_add _ _ _
-  add_smul s t P := show span R (s ⊔ t) * P = _ by erw [span_union, right_distrib]
-  mul_smul s t P := show _ = _ * (_ * _) by rw [← mul_assoc, span_mul_span, ← image_mul_prod]
-  one_smul P :=
-    show span R {(1 : A)} * P = _ by
-      conv_lhs => erw [← span_eq P]
-      erw [span_mul_span, one_mul, span_eq]
-  zero_smul P := show span R ∅ * P = ⊥ by erw [span_empty, bot_mul]
+  add_smul s t P := by simp_rw [SMul.smul, SetSemiring.down_add, span_union, sup_mul, add_eq_sup]
+  mul_smul s t P := by simp_rw [SMul.smul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
+  one_smul P := by simp_rw [SMul.smul, SetSemiring.down_one, ← one_eq_span_one_set, one_mul]
+  zero_smul P := by simp_rw [SMul.smul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
   smul_zero _ := mul_bot _
 #align submodule.module_set Submodule.moduleSet
 
 variable {R A}
 
-theorem smul_def {s : SetSemiring A} {P : Submodule R A} : s • P = span R s * P :=
+theorem smul_def (s : SetSemiring A) (P : Submodule R A) : s • P = span R s.down * P :=
   rfl
 #align submodule.smul_def Submodule.smul_def
 
-theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A} (h₁ : s.down ≤ t.down)
+theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A} (h₁ : s.down ⊆ t.down)
     (h₂ : M ≤ N) : s • M ≤ t • N :=
   mul_le_mul (span_mono h₁) h₂
 #align submodule.smul_le_smul Submodule.smul_le_smul

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

@@ -261,7 +261,7 @@ theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
 #align submodule.sup_mul Submodule.sup_mul
 
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
-  image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
+  image2_subset_map₂ (LinearMap.Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :

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

A mix of various changes; generated with a script and manually tweaked.

@@ -36,7 +36,7 @@ Let `R` be a commutative ring (or semiring) and let `A` be an `R`-algebra.
 
 It is proved that `Submodule R A` is a semiring, and also an algebra over `Set A`.
 
-Additionally, in the `pointwise` locale we promote `Submodule.pointwiseDistribMulAction` to a
+Additionally, in the `Pointwise` locale we promote `Submodule.pointwiseDistribMulAction` to a
 `MulSemiringAction` as `Submodule.pointwiseMulSemiringAction`.
 
 ## Tags
@@ -607,7 +607,7 @@ variable {α : Type*} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A
 
 /-- The action on a submodule corresponding to applying the action to every element.
 
-This is available as an instance in the `pointwise` locale.
+This is available as an instance in the `Pointwise` locale.
 
 This is a stronger version of `Submodule.pointwiseDistribMulAction`. -/
 protected def pointwiseMulSemiringAction : MulSemiringAction α (Submodule R A) :=

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -458,7 +458,7 @@ theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.
   · exact (h rfl).elim
   · rw [pow_succ, pow_succ, mul_toAddSubmonoid]
     cases n with
-    | zero => rw [pow_zero, pow_zero, mul_one, ← mul_toAddSubmonoid, mul_one]
+    | zero => rw [pow_zero, pow_zero, one_mul, ← mul_toAddSubmonoid, one_mul]
     | succ n => rw [ih n.succ_ne_zero]
 #align submodule.pow_to_add_submonoid Submodule.pow_toAddSubmonoid
 
@@ -474,7 +474,8 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
     (algebraMap : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
     (add : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
-    (mem_mul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x) (mul_mem_mul hm hx))
+    (mem_mul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x)
+      ((pow_succ' M i).symm ▸ (mul_mem_mul hm hx)))
     -- Porting note: swapped argument order to match order of `C`
     {n : ℕ} {x : A}
     (hx : x ∈ M ^ n) : C n x hx := by
@@ -482,6 +483,9 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
   · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx
     exact algebraMap r
+  revert hx
+  simp_rw [pow_succ']
+  intro hx
   exact
     Submodule.mul_induction_on' (fun m hm x ih => mem_mul _ hm _ _ _ (n_ih ih))
       (fun x hx y hy Cx Cy => add _ _ _ _ _ Cx Cy) hx
@@ -494,7 +498,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     (add : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
     (mul_mem :
       ∀ i x hx, C i x hx →
-        ∀ m (hm : m ∈ M), C i.succ (x * m) ((pow_succ' M i).symm ▸ mul_mem_mul hx hm))
+        ∀ m (hm : m ∈ M), C i.succ (x * m) (mul_mem_mul hx hm))
     -- Porting note: swapped argument order to match order of `C`
     {n : ℕ} {x : A} (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
@@ -502,7 +506,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     obtain ⟨r, rfl⟩ := hx
     exact algebraMap r
   revert hx
-  simp_rw [pow_succ']
+  simp_rw [pow_succ]
   intro hx
   exact
     Submodule.mul_induction_on' (fun m hm x ih => mul_mem _ _ hm (n_ih _) _ ih)

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -70,13 +70,11 @@ end SubMulAction
 namespace Submodule
 
 variable {ι : Sort uι}
-
 variable {R : Type u} [CommSemiring R]
 
 section Ring
 
 variable {A : Type v} [Semiring A] [Algebra R A]
-
 variable (S T : Set A) {M N P Q : Submodule R A} {m n : A}
 
 /-- `1 : Submodule R A` is the submodule R of A. -/
@@ -204,7 +202,6 @@ theorem span_mul_span : span R S * span R T = span R (S * T) :=
 #align submodule.span_mul_span Submodule.span_mul_span
 
 variable {R}
-
 variable (M N P Q)
 
 @[simp]
@@ -625,7 +622,6 @@ end Ring
 section CommRing
 
 variable {A : Type v} [CommSemiring A] [Algebra R A]
-
 variable {M N : Submodule R A} {m n : A}
 
 theorem mul_mem_mul_rev (hm : m ∈ M) (hn : n ∈ N) : n * m ∈ M * N :=

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -346,7 +346,7 @@ end
 
 section DecidableEq
 
-open Classical
+open scoped Classical
 
 theorem mem_span_mul_finite_of_mem_span_mul {R A} [Semiring R] [AddCommMonoid A] [Mul A]
     [Module R A] {S : Set A} {S' : Set A} {x : A} (hx : x ∈ span R (S * S')) :

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -81,7 +81,7 @@ variable (S T : Set A) {M N P Q : Submodule R A} {m n : A}
 
 /-- `1 : Submodule R A` is the submodule R of A. -/
 instance one : One (Submodule R A) :=
-  -- porting note: `f.range` notation doesn't work
+  -- Porting note: `f.range` notation doesn't work
   ⟨LinearMap.range (Algebra.linearMap R A)⟩
 #align submodule.has_one Submodule.one
 
@@ -119,7 +119,7 @@ theorem one_eq_span_one_set : (1 : Submodule R A) = span R 1 :=
 #align submodule.one_eq_span_one_set Submodule.one_eq_span_one_set
 
 theorem one_le : (1 : Submodule R A) ≤ P ↔ (1 : A) ∈ P := by
-  -- porting note: simpa no longer closes refl goals, so added `SetLike.mem_coe`
+  -- Porting note: simpa no longer closes refl goals, so added `SetLike.mem_coe`
   simp only [one_eq_span, span_le, Set.singleton_subset_iff, SetLike.mem_coe]
 #align submodule.one_le Submodule.one_le
 
@@ -172,7 +172,7 @@ theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
 
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid := by
-  dsimp [HMul.hMul, Mul.mul]  --porting note: added `hMul`
+  dsimp [HMul.hMul, Mul.mul]  -- Porting note: added `hMul`
   rw [map₂, iSup_toAddSubmonoid]
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
@@ -267,12 +267,12 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
       apply congr_arg sSup
       ext S
       constructor <;> rintro ⟨y, hy⟩
-      · use ⟨f y, mem_map.mpr ⟨y.1, y.2, rfl⟩⟩  -- porting note: added `⟨⟩`
+      · use ⟨f y, mem_map.mpr ⟨y.1, y.2, rfl⟩⟩  -- Porting note: added `⟨⟩`
         refine' Eq.trans _ hy
         ext
         simp
       · obtain ⟨y', hy', fy_eq⟩ := mem_map.mp y.2
-        use ⟨y', hy'⟩  -- porting note: added `⟨⟩`
+        use ⟨y', hy'⟩  -- Porting note: added `⟨⟩`
         refine' Eq.trans _ hy
         rw [f.toLinearMap_apply] at fy_eq
         ext
@@ -382,13 +382,13 @@ theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈
 variable {M N P}
 
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x := by
-  --porting note: need both `*` and `Mul.mul`
+  -- Porting note: need both `*` and `Mul.mul`
   simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map]
   rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
 
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x := by
-  --porting note: need both `*` and `Mul.mul`
+  -- Porting note: need both `*` and `Mul.mul`
   simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map_flip]
   rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
@@ -434,7 +434,7 @@ instance idemSemiring : IdemSemiring (Submodule R A) :=
     mul_zero := mul_bot
     left_distrib := mul_sup
     right_distrib := sup_mul,
-    -- porting note: removed `(by infer_instance : OrderBot (Submodule R A))`
+    -- Porting note: removed `(by infer_instance : OrderBot (Submodule R A))`
     bot_le := fun _ => bot_le }
 
 variable (M)
@@ -478,7 +478,7 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
     (algebraMap : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
     (add : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
     (mem_mul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x) (mul_mem_mul hm hx))
-    -- porting note: swapped argument order to match order of `C`
+    -- Porting note: swapped argument order to match order of `C`
     {n : ℕ} {x : A}
     (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
@@ -498,7 +498,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     (mul_mem :
       ∀ i x hx, C i x hx →
         ∀ m (hm : m ∈ M), C i.succ (x * m) ((pow_succ' M i).symm ▸ mul_mem_mul hx hm))
-    -- porting note: swapped argument order to match order of `C`
+    -- Porting note: swapped argument order to match order of `C`
     {n : ℕ} {x : A} (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
   · rw [pow_zero] at hx
@@ -518,7 +518,7 @@ is closed under addition, and holds for `m * x` where `m ∈ M` and it holds for
 protected theorem pow_induction_on_left {C : A → Prop} (hr : ∀ r : R, C (algebraMap _ _ r))
     (hadd : ∀ x y, C x → C y → C (x + y)) (hmul : ∀ m ∈ M, ∀ (x), C x → C (m * x)) {x : A} {n : ℕ}
     (hx : x ∈ M ^ n) : C x :=
-  -- porting note: `M` is explicit yet can't be passed positionally!
+  -- Porting note: `M` is explicit yet can't be passed positionally!
   Submodule.pow_induction_on_left' (M := M) (C := fun _ a _ => C a) hr
     (fun x y _i _hx _hy => hadd x y)
     (fun _m hm _i _x _hx => hmul _ hm _) hx
@@ -596,7 +596,7 @@ def span.ringHom : SetSemiring A →+* Submodule R A where
   map_one' := one_eq_span.symm
   map_add' := span_union
   map_mul' s t := by
-    dsimp only -- porting note: new, needed due to new-style structures
+    dsimp only -- Porting note: new, needed due to new-style structures
     rw [SetSemiring.down_mul, span_mul_span]
 #align submodule.span.ring_hom Submodule.span.ringHom
 
@@ -661,7 +661,7 @@ variable (R A)
 
 /-- R-submodules of the R-algebra A are a module over `Set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A) where
-  -- porting note: have to unfold both `HSMul.hSMul` and `SMul.smul`
+  -- Porting note: have to unfold both `HSMul.hSMul` and `SMul.smul`
   -- Note: the hint `(α := A)` is new in #8386
   smul s P := span R (SetSemiring.down (α := A) s) * P
   smul_add _ _ _ := mul_add _ _ _
@@ -745,7 +745,7 @@ theorem one_le_one_div {I : Submodule R A} : 1 ≤ 1 / I ↔ I ≤ 1 := by
 #align submodule.one_le_one_div Submodule.one_le_one_div
 
 theorem le_self_mul_one_div {I : Submodule R A} (hI : I ≤ 1) : I ≤ I * (1 / I) := by
-  refine (mul_one I).symm.trans_le ?_  -- porting note: drop `rw {occs := _}` in favor of `refine`
+  refine (mul_one I).symm.trans_le ?_  -- Porting note: drop `rw {occs := _}` in favor of `refine`
   apply mul_le_mul_right (one_le_one_div.mpr hI)
 #align submodule.le_self_mul_one_div Submodule.le_self_mul_one_div
 

In order to improve the ergonomics of the induction tactic, this renames the arguments of:

• ExteriorAlgebra.induction
• TensorAlgebra.induction
• CliffordAlgebra.induction
• CliffordAlgebra.left_induction
• CliffordAlgebra.right_induction
• CliffordAlgebra.even_induction
• CliffordAlgebra.odd_induction
• Submodule.iSup_induction'
• Submodule.pow_induction_on_left'
• Submodule.pow_induction_on_right'

This is slightly awkward for name-resolution within these induction principles, as the argument names end up clashing with the function they are about. Thankfully, this pain is not transferred to the caller using induction _ using _.

@@ -187,13 +187,14 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
 protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
-    (hm : ∀ m (hm : m ∈ M) n (hn : n ∈ N), C (m * n) (mul_mem_mul hm hn))
-    (ha : ∀ x hx y hy, C x hx → C y hy → C (x + y) (add_mem hx hy)) {r : A} (hr : r ∈ M * N) :
+    (mem_mul_mem : ∀ m (hm : m ∈ M) n (hn : n ∈ N), C (m * n) (mul_mem_mul hm hn))
+    (add : ∀ x hx y hy, C x hx → C y hy → C (x + y) (add_mem hx hy)) {r : A} (hr : r ∈ M * N) :
     C r hr := by
   refine' Exists.elim _ fun (hr : r ∈ M * N) (hc : C r hr) => hc
   exact
-    Submodule.mul_induction_on hr (fun x hx y hy => ⟨_, hm _ hx _ hy⟩) fun x y ⟨_, hx⟩ ⟨_, hy⟩ =>
-      ⟨_, ha _ _ _ _ hx hy⟩
+    Submodule.mul_induction_on hr
+      (fun x hx y hy => ⟨_, mem_mul_mem _ hx _ hy⟩)
+      fun x y ⟨_, hx⟩ ⟨_, hy⟩ => ⟨_, add _ _ _ _ hx hy⟩
 #align submodule.mul_induction_on' Submodule.mul_induction_on'
 
 variable (R)
@@ -474,27 +475,27 @@ theorem le_pow_toAddSubmonoid {n : ℕ} : M.toAddSubmonoid ^ n ≤ (M ^ n).toAdd
 /-- Dependent version of `Submodule.pow_induction_on_left`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
-    (hr : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
-    (hadd : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
-    (hmul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x) (mul_mem_mul hm hx))
+    (algebraMap : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
+    (add : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
+    (mem_mul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x) (mul_mem_mul hm hx))
     -- porting note: swapped argument order to match order of `C`
     {n : ℕ} {x : A}
     (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
   · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx
-    exact hr r
+    exact algebraMap r
   exact
-    Submodule.mul_induction_on' (fun m hm x ih => hmul _ hm _ _ _ (n_ih ih))
-      (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
+    Submodule.mul_induction_on' (fun m hm x ih => mem_mul _ hm _ _ _ (n_ih ih))
+      (fun x hx y hy Cx Cy => add _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_left' Submodule.pow_induction_on_left'
 
 /-- Dependent version of `Submodule.pow_induction_on_right`. -/
 @[elab_as_elim]
 protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n → Prop}
-    (hr : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
-    (hadd : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
-    (hmul :
+    (algebraMap : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
+    (add : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
+    (mul_mem :
       ∀ i x hx, C i x hx →
         ∀ m (hm : m ∈ M), C i.succ (x * m) ((pow_succ' M i).symm ▸ mul_mem_mul hx hm))
     -- porting note: swapped argument order to match order of `C`
@@ -502,13 +503,13 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
   induction' n with n n_ih generalizing x
   · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx
-    exact hr r
+    exact algebraMap r
   revert hx
   simp_rw [pow_succ']
   intro hx
   exact
-    Submodule.mul_induction_on' (fun m hm x ih => hmul _ _ hm (n_ih _) _ ih)
-      (fun x hx y hy Cx Cy => hadd _ _ _ _ _ Cx Cy) hx
+    Submodule.mul_induction_on' (fun m hm x ih => mul_mem _ _ hm (n_ih _) _ ih)
+      (fun x hx y hy Cx Cy => add _ _ _ _ _ Cx Cy) hx
 #align submodule.pow_induction_on_right' Submodule.pow_induction_on_right'
 
 /-- To show a property on elements of `M ^ n` holds, it suffices to show that it holds for scalars,

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -216,13 +216,13 @@ theorem bot_mul : ⊥ * M = ⊥ :=
   map₂_bot_left _ _
 #align submodule.bot_mul Submodule.bot_mul
 
--- @[simp] -- Porting note: simp can prove this once we have a monoid structure
+-- @[simp] -- Porting note (#10618): simp can prove this once we have a monoid structure
 protected theorem one_mul : (1 : Submodule R A) * M = M := by
   conv_lhs => rw [one_eq_span, ← span_eq M]
   erw [span_mul_span, one_mul, span_eq]
 #align submodule.one_mul Submodule.one_mul
 
--- @[simp] -- Porting note: simp can prove this once we have a monoid structure
+-- @[simp] -- Porting note (#10618): simp can prove this once we have a monoid structure
 protected theorem mul_one : M * 1 = M := by
   conv_lhs => rw [one_eq_span, ← span_eq M]
   erw [span_mul_span, mul_one, span_eq]

Remove unnecessary "rw"s.

@@ -596,7 +596,7 @@ def span.ringHom : SetSemiring A →+* Submodule R A where
   map_add' := span_union
   map_mul' s t := by
     dsimp only -- porting note: new, needed due to new-style structures
-    rw [SetSemiring.down_mul, span_mul_span, ← image_mul_prod]
+    rw [SetSemiring.down_mul, span_mul_span]
 #align submodule.span.ring_hom Submodule.span.ringHom
 
 section

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

@@ -6,15 +6,16 @@ Authors: Kenny Lau
 import Mathlib.Algebra.Algebra.Bilinear
 import Mathlib.Algebra.Algebra.Equiv
 import Mathlib.Algebra.Algebra.Opposite
-import Mathlib.Algebra.Module.Submodule.Pointwise
-import Mathlib.Algebra.Module.Submodule.Bilinear
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 import Mathlib.Algebra.Module.Opposites
+import Mathlib.Algebra.Module.Submodule.Bilinear
+import Mathlib.Algebra.Module.Submodule.Pointwise
 import Mathlib.Algebra.Order.Kleene
 import Mathlib.Data.Finset.Pointwise
-import Mathlib.Data.Set.Semiring
 import Mathlib.Data.Set.Pointwise.BigOperators
+import Mathlib.Data.Set.Semiring
 import Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise
-import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
+import Mathlib.LinearAlgebra.Basic
 
 #align_import algebra.algebra.operations from "leanprover-community/mathlib"@"27b54c47c3137250a521aa64e9f1db90be5f6a26"
 

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

simp not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -94,7 +94,7 @@ theorem le_one_toAddSubmonoid : 1 ≤ (1 : Submodule R A).toAddSubmonoid := by
 #align submodule.le_one_to_add_submonoid Submodule.le_one_toAddSubmonoid
 
 theorem algebraMap_mem (r : R) : algebraMap R A r ∈ (1 : Submodule R A) :=
-  LinearMap.mem_range_self _ _
+  LinearMap.mem_range_self (Algebra.linearMap R A) _
 #align submodule.algebra_map_mem Submodule.algebraMap_mem
 
 @[simp]
@@ -588,7 +588,8 @@ theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 on either side). -/
 @[simps]
 def span.ringHom : SetSemiring A →+* Submodule R A where
-  toFun s := Submodule.span R (SetSemiring.down s)
+  -- Note: the hint `(α := A)` is new in #8386
+  toFun s := Submodule.span R (SetSemiring.down (α := A) s)
   map_zero' := span_empty
   map_one' := one_eq_span.symm
   map_add' := span_union
@@ -659,7 +660,8 @@ variable (R A)
 /-- R-submodules of the R-algebra A are a module over `Set A`. -/
 instance moduleSet : Module (SetSemiring A) (Submodule R A) where
   -- porting note: have to unfold both `HSMul.hSMul` and `SMul.smul`
-  smul s P := span R (SetSemiring.down s) * P
+  -- Note: the hint `(α := A)` is new in #8386
+  smul s P := span R (SetSemiring.down (α := A) s) * P
   smul_add _ _ _ := mul_add _ _ _
   add_smul s t P := by
     simp_rw [HSMul.hSMul, SetSemiring.down_add, span_union, sup_mul, add_eq_sup]
@@ -675,12 +677,12 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A) where
 variable {R A}
 
 theorem smul_def (s : SetSemiring A) (P : Submodule R A) :
-    s • P = span R (SetSemiring.down s) * P :=
+    s • P = span R (SetSemiring.down (α := A) s) * P :=
   rfl
 #align submodule.smul_def Submodule.smul_def
 
 theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A}
-    (h₁ : SetSemiring.down s ⊆ SetSemiring.down t)
+    (h₁ : SetSemiring.down (α := A) s ⊆ SetSemiring.down (α := A) t)
     (h₂ : M ≤ N) : s • M ≤ t • N :=
   mul_le_mul (span_mono h₁) h₂
 #align submodule.smul_le_smul Submodule.smul_le_smul

This PR defines the absolute ideal norm of a fractional ideal I : FractionalIdeal R⁰ K where K is a fraction field of R as a zero-preserving group homomorphism with values in ℚ and proves that it generalises the norm on (integral) ideals (and some other classical result).

Also in this PR:

• Add the directory Mathlib/RingTheory/FractionalIdeal and move the file Mathlib/RingTheory/FractionalIdeal.lean to Mathlib/RingTheory/FractionalIdeal/Basic.lean. The new results are in Mathlib/RingTheory/FractionalIdeal/Norm.lean
• Define the numerator and denominator of a fractional ideal. These are used to define the norm. Also define a linear equiv between a fractional ideal and its numerator.
• Several technical lemmas.

@@ -405,6 +405,21 @@ lemma mul_mem_smul_iff {S} [CommRing S] [Algebra R S] {x : S} {p : Submodule R S
     x * y ∈ x • p ↔ y ∈ p :=
   show Exists _ ↔ _ by simp [mul_cancel_left_mem_nonZeroDivisors hx]
 
+variable (M N) in
+theorem mul_smul_mul_eq_smul_mul_smul (x y : R) : (x * y) • (M * N) = (x • M) * (y • N) := by
+  ext
+  refine ⟨?_, fun hx ↦ Submodule.mul_induction_on hx ?_ fun _ _ hx hy ↦ Submodule.add_mem _ hx hy⟩
+  · rintro ⟨_, hx, rfl⟩
+    rw [DistribMulAction.toLinearMap_apply]
+    refine Submodule.mul_induction_on hx (fun m hm n hn ↦ ?_) (fun _ _ hn hm ↦ ?_)
+    · rw [← smul_mul_smul x y m n]
+      exact mul_mem_mul (smul_mem_pointwise_smul m x M hm) (smul_mem_pointwise_smul n y N hn)
+    · rw [smul_add]
+      exact Submodule.add_mem _ hn hm
+  · rintro _ ⟨m, hm, rfl⟩ _ ⟨n, hn, rfl⟩
+    erw [smul_mul_smul x y m n]
+    exact smul_mem_pointwise_smul _ _ _ (mul_mem_mul hm hn)
+
 /-- Sub-R-modules of an R-algebra form an idempotent semiring. -/
 instance idemSemiring : IdemSemiring (Submodule R A) :=
   { toAddSubmonoid_injective.semigroup _ fun m n : Submodule R A => mul_toAddSubmonoid m n,

Golf the proof of Submodule.smul_singleton and rename it to Submodule.singleton_smul.

@@ -670,19 +670,12 @@ theorem smul_le_smul {s t : SetSemiring A} {M N : Submodule R A}
   mul_le_mul (span_mono h₁) h₂
 #align submodule.smul_le_smul Submodule.smul_le_smul
 
-theorem smul_singleton (a : A) (M : Submodule R A) :
+theorem singleton_smul (a : A) (M : Submodule R A) :
     Set.up ({a} : Set A) • M = M.map (LinearMap.mulLeft R a) := by
   conv_lhs => rw [← span_eq M]
-  change span _ _ * span _ _ = _
-  rw [span_mul_span]
-  apply le_antisymm
-  · rw [span_le]
-    rintro _ ⟨b, m, hb, hm, rfl⟩
-    rw [SetLike.mem_coe, mem_map, Set.mem_singleton_iff.mp hb]
-    exact ⟨m, hm, rfl⟩
-  · rintro _ ⟨m, hm, rfl⟩
-    exact subset_span ⟨a, m, Set.mem_singleton a, hm, rfl⟩
-#align submodule.smul_singleton Submodule.smul_singleton
+  rw [smul_def, SetSemiring.down_up, span_mul_span, singleton_mul]
+  exact (map (LinearMap.mulLeft R a) M).span_eq
+#align submodule.smul_singleton Submodule.singleton_smul
 
 section Quotient
 

Search for [∀∃].*(_ and manually replace some occurrences with more readable versions. In case of ∀, the new expressions are defeq to the old ones. In case of ∃, they differ by exists_prop.

In some rare cases, golf proofs that needed fixing.

@@ -186,8 +186,8 @@ protected theorem mul_induction_on {C : A → Prop} {r : A} (hr : r ∈ M * N)
 /-- A dependent version of `mul_induction_on`. -/
 @[elab_as_elim]
 protected theorem mul_induction_on' {C : ∀ r, r ∈ M * N → Prop}
-    (hm : ∀ m (_ : m ∈ M), ∀ n (_ : n ∈ N), C (m * n) (mul_mem_mul ‹_› ‹_›))
-    (ha : ∀ x hx y hy, C x hx → C y hy → C (x + y) (add_mem ‹_› ‹_›)) {r : A} (hr : r ∈ M * N) :
+    (hm : ∀ m (hm : m ∈ M) n (hn : n ∈ N), C (m * n) (mul_mem_mul hm hn))
+    (ha : ∀ x hx y hy, C x hx → C y hy → C (x + y) (add_mem hx hy)) {r : A} (hr : r ∈ M * N) :
     C r hr := by
   refine' Exists.elim _ fun (hr : r ∈ M * N) (hc : C r hr) => hc
   exact

@@ -14,6 +14,7 @@ import Mathlib.Data.Finset.Pointwise
 import Mathlib.Data.Set.Semiring
 import Mathlib.Data.Set.Pointwise.BigOperators
 import Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise
+import Mathlib.Algebra.GroupWithZero.NonZeroDivisors
 
 #align_import algebra.algebra.operations from "leanprover-community/mathlib"@"27b54c47c3137250a521aa64e9f1db90be5f6a26"
 
@@ -390,6 +391,20 @@ theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P,
   rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
 
+lemma span_singleton_mul {x : A} {p : Submodule R A} :
+    Submodule.span R {x} * p = x • p := ext fun _ ↦ mem_span_singleton_mul
+
+lemma mem_smul_iff_inv_mul_mem {S} [Field S] [Algebra R S] {x : S} {p : Submodule R S} {y : S}
+    (hx : x ≠ 0) : y ∈ x • p ↔ x⁻¹ * y ∈ p := by
+  constructor
+  · rintro ⟨a, ha : a ∈ p, rfl⟩; simpa [inv_mul_cancel_left₀ hx]
+  · exact fun h ↦ ⟨_, h, by simp [mul_inv_cancel_left₀ hx]⟩
+
+lemma mul_mem_smul_iff {S} [CommRing S] [Algebra R S] {x : S} {p : Submodule R S} {y : S}
+    (hx : x ∈ nonZeroDivisors S) :
+    x * y ∈ x • p ↔ y ∈ p :=
+  show Exists _ ↔ _ by simp [mul_cancel_left_mem_nonZeroDivisors hx]
+
 /-- Sub-R-modules of an R-algebra form an idempotent semiring. -/
 instance idemSemiring : IdemSemiring (Submodule R A) :=
   { toAddSubmonoid_injective.semigroup _ fun m n : Submodule R A => mul_toAddSubmonoid m n,

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

@@ -636,7 +636,7 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A) where
   mul_smul s t P := by
     simp_rw [HSMul.hSMul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
   one_smul P := by
-    simp_rw [HSMul.hSMul, SetSemiring.down_one, ←one_eq_span_one_set, one_mul]
+    simp_rw [HSMul.hSMul, SetSemiring.down_one, ← one_eq_span_one_set, one_mul]
   zero_smul P := by
     simp_rw [HSMul.hSMul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
   smul_zero _ := mul_bot _

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -316,6 +316,16 @@ theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
   simp_rw [comap_equiv_eq_map_symm, map_unop_mul]
 #align submodule.comap_op_mul Submodule.comap_op_mul
 
+lemma restrictScalars_mul {A B C} [CommSemiring A] [CommSemiring B] [Semiring C]
+    [Algebra A B] [Algebra A C] [Algebra B C] [IsScalarTower A B C] {I J : Submodule B C} :
+  (I * J).restrictScalars A = I.restrictScalars A * J.restrictScalars A := by
+  apply le_antisymm
+  · intro x (hx : x ∈ I * J)
+    refine Submodule.mul_induction_on hx ?_ ?_
+    · exact fun m hm n hn ↦ mul_mem_mul hm hn
+    · exact fun _ _ ↦ add_mem
+  · exact mul_le.mpr (fun _ hm _ hn ↦ mul_mem_mul hm hn)
+
 section
 
 open Pointwise

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

@@ -294,8 +294,8 @@ theorem map_op_mul :
 theorem comap_unop_mul :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) N *
-        comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M :=
-  by simp_rw [← map_equiv_eq_comap_symm, map_op_mul]
+        comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M := by
+  simp_rw [← map_equiv_eq_comap_symm, map_op_mul]
 #align submodule.comap_unop_mul Submodule.comap_unop_mul
 
 theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
@@ -312,8 +312,8 @@ theorem map_unop_mul (M N : Submodule R Aᵐᵒᵖ) :
 theorem comap_op_mul (M N : Submodule R Aᵐᵒᵖ) :
     comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M * N) =
       comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) N *
-        comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M :=
-  by simp_rw [comap_equiv_eq_map_symm, map_unop_mul]
+        comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M := by
+  simp_rw [comap_equiv_eq_map_symm, map_unop_mul]
 #align submodule.comap_op_mul Submodule.comap_op_mul
 
 section
@@ -534,14 +534,14 @@ theorem comap_op_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
 
 theorem map_op_pow (n : ℕ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (M ^ n) =
-      map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n :=
-  by rw [map_equiv_eq_comap_symm, map_equiv_eq_comap_symm, comap_unop_pow]
+      map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) M ^ n := by
+  rw [map_equiv_eq_comap_symm, map_equiv_eq_comap_symm, comap_unop_pow]
 #align submodule.map_op_pow Submodule.map_op_pow
 
 theorem map_unop_pow (n : ℕ) (M : Submodule R Aᵐᵒᵖ) :
     map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) (M ^ n) =
-      map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n :=
-  by rw [← comap_equiv_eq_map_symm, ← comap_equiv_eq_map_symm, comap_op_pow]
+      map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ).symm : Aᵐᵒᵖ →ₗ[R] A) M ^ n := by
+  rw [← comap_equiv_eq_map_symm, ← comap_equiv_eq_map_symm, comap_op_pow]
 #align submodule.map_unop_pow Submodule.map_unop_pow
 
 /-- `span` is a semiring homomorphism (recall multiplication is pointwise multiplication of subsets

This incorporates changes from

• #7845
• #7847
• #7853
• #7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

@@ -463,10 +463,7 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     obtain ⟨r, rfl⟩ := hx
     exact hr r
   revert hx
-  -- porting note: workaround for lean4#1926, was `simp_rw [pow_succ']`
-  suffices h_lean4_1926 : ∀ (hx' : x ∈ M ^ n * M), C (Nat.succ n) x (by rwa [pow_succ']) from
-    fun hx => h_lean4_1926 (by rwa [← pow_succ'])
-  -- porting note: end workaround
+  simp_rw [pow_succ']
   intro hx
   exact
     Submodule.mul_induction_on' (fun m hm x ih => hmul _ _ hm (n_ih _) _ ih)

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

@@ -638,7 +638,7 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A) where
 variable {R A}
 
 theorem smul_def (s : SetSemiring A) (P : Submodule R A) :
-  s • P = span R (SetSemiring.down s) * P :=
+    s • P = span R (SetSemiring.down s) * P :=
   rfl
 #align submodule.smul_def Submodule.smul_def
 

This moves the Algebra instance on MulOpposite to a new file, and adds the AlgHom and AlgEquiv versions of various existing RingHom and RingEquiv definitions:

• AlgHom.fromOpposite
• AlgHom.toOpposite
• AlgHom.op
• AlgHom.unop
• AlgEquiv.op
• AlgHom.unop
• AlgEquiv.toOpposite

As MulOpposite.instAlgebra is no longer in Mathlib.Algebra.Algebra.Basic, some new downstream imports are needed.

@@ -5,6 +5,7 @@ Authors: Kenny Lau
 -/
 import Mathlib.Algebra.Algebra.Bilinear
 import Mathlib.Algebra.Algebra.Equiv
+import Mathlib.Algebra.Algebra.Opposite
 import Mathlib.Algebra.Module.Submodule.Pointwise
 import Mathlib.Algebra.Module.Submodule.Bilinear
 import Mathlib.Algebra.Module.Opposites

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

This has nice performance benefits.

@@ -561,7 +561,7 @@ def span.ringHom : SetSemiring A →+* Submodule R A where
 
 section
 
-variable {α : Type _} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A]
+variable {α : Type*} [Monoid α] [MulSemiringAction α A] [SMulCommClass α R A]
 
 /-- The action on a submodule corresponding to applying the action to every element.
 
@@ -602,7 +602,7 @@ protected theorem mul_comm : M * N = N * M :=
 instance : IdemCommSemiring (Submodule R A) :=
   { Submodule.idemSemiring with mul_comm := Submodule.mul_comm }
 
-theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
+theorem prod_span {ι : Type*} (s : Finset ι) (M : ι → Set A) :
     (∏ i in s, Submodule.span R (M i)) = Submodule.span R (∏ i in s, M i) := by
   letI := Classical.decEq ι
   refine' Finset.induction_on s _ _
@@ -611,7 +611,7 @@ theorem prod_span {ι : Type _} (s : Finset ι) (M : ι → Set A) :
     rw [Finset.prod_insert H, Finset.prod_insert H, ih, span_mul_span]
 #align submodule.prod_span Submodule.prod_span
 
-theorem prod_span_singleton {ι : Type _} (s : Finset ι) (x : ι → A) :
+theorem prod_span_singleton {ι : Type*} (s : Finset ι) (x : ι → A) :
     (∏ i in s, span R ({x i} : Set A)) = span R {∏ i in s, x i} := by
   rw [prod_span, Set.finset_prod_singleton]
 #align submodule.prod_span_singleton Submodule.prod_span_singleton
@@ -723,7 +723,7 @@ theorem mul_one_div_le_one {I : Submodule R A} : I * (1 / I) ≤ 1 := by
 #align submodule.mul_one_div_le_one Submodule.mul_one_div_le_one
 
 @[simp]
-protected theorem map_div {B : Type _} [CommSemiring B] [Algebra R B] (I J : Submodule R A)
+protected theorem map_div {B : Type*} [CommSemiring B] [Algebra R B] (I J : Submodule R A)
     (h : A ≃ₐ[R] B) : (I / J).map h.toLinearMap = I.map h.toLinearMap / J.map h.toLinearMap := by
   ext x
   simp only [mem_map, mem_div_iff_forall_mul_mem]

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2019 Kenny Lau. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kenny Lau
-
-! This file was ported from Lean 3 source module algebra.algebra.operations
-! leanprover-community/mathlib commit 27b54c47c3137250a521aa64e9f1db90be5f6a26
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Bilinear
 import Mathlib.Algebra.Algebra.Equiv
@@ -19,6 +14,8 @@ import Mathlib.Data.Set.Semiring
 import Mathlib.Data.Set.Pointwise.BigOperators
 import Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise
 
+#align_import algebra.algebra.operations from "leanprover-community/mathlib"@"27b54c47c3137250a521aa64e9f1db90be5f6a26"
+
 /-!
 # Multiplication and division of submodules of an algebra.
 

Changes are of the form

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

@@ -289,7 +289,7 @@ theorem map_op_mul :
     show op n * op m ∈ _
     exact mul_mem_mul hn hm
   · refine' mul_le.2 (MulOpposite.rec' fun m hm => MulOpposite.rec' fun n hn => _)
-    rw [Submodule.mem_map_equiv] at hm hn⊢
+    rw [Submodule.mem_map_equiv] at hm hn ⊢
     exact mul_mem_mul hn hm
 #align submodule.map_op_mul Submodule.map_op_mul
 

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

@@ -81,7 +81,7 @@ variable (S T : Set A) {M N P Q : Submodule R A} {m n : A}
 
 /-- `1 : Submodule R A` is the submodule R of A. -/
 instance one : One (Submodule R A) :=
--- porting note: `f.range` notation doesn't work
+  -- porting note: `f.range` notation doesn't work
   ⟨LinearMap.range (Algebra.linearMap R A)⟩
 #align submodule.has_one Submodule.one
 

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>

@@ -438,7 +438,8 @@ protected theorem pow_induction_on_left' {C : ∀ (n : ℕ) (x), x ∈ M ^ n →
     (hr : ∀ r : R, C 0 (algebraMap _ _ r) (algebraMap_mem r))
     (hadd : ∀ x y i hx hy, C i x hx → C i y hy → C i (x + y) (add_mem ‹_› ‹_›))
     (hmul : ∀ m (hm : m ∈ M), ∀ (i x hx), C i x hx → C i.succ (m * x) (mul_mem_mul hm hx))
-    {x : A} {n : ℕ}
+    -- porting note: swapped argument order to match order of `C`
+    {n : ℕ} {x : A}
     (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
   · rw [pow_zero] at hx
@@ -457,7 +458,8 @@ protected theorem pow_induction_on_right' {C : ∀ (n : ℕ) (x), x ∈ M ^ n 
     (hmul :
       ∀ i x hx, C i x hx →
         ∀ m (hm : m ∈ M), C i.succ (x * m) ((pow_succ' M i).symm ▸ mul_mem_mul hx hm))
-    {x : A} {n : ℕ} (hx : x ∈ M ^ n) : C n x hx := by
+    -- porting note: swapped argument order to match order of `C`
+    {n : ℕ} {x : A} (hx : x ∈ M ^ n) : C n x hx := by
   induction' n with n n_ih generalizing x
   · rw [pow_zero] at hx
     obtain ⟨r, rfl⟩ := hx

@@ -322,21 +322,11 @@ section
 
 open Pointwise
 
-/-
-Porting note: the following def ought to be
-```
-protected def hasDistribPointwiseNeg {A} [Ring A] [Algebra R A] : HasDistribNeg (Submodule R A) :=
-  toAddSubmonoid_injective.hasDistribNeg _ neg_toAddSubmonoid mul_toAddSubmonoid
-```
-but this is not possible due to η-for-classes issues. See lean4#2074
--/
 /-- `Submodule.pointwiseNeg` distributes over multiplication.
 
-This is available as an instance in the `pointwise` locale. -/
-protected def hasDistribPointwiseNeg {A} [Ring A] [Algebra R A] :
-    HasDistribNeg (@Submodule R A _ _ Algebra.toModule) :=
-  @Function.Injective.hasDistribNeg _ _ _ _ (id _) _ _ toAddSubmonoid_injective
-    (@neg_toAddSubmonoid R A _ _ Algebra.toModule) mul_toAddSubmonoid
+This is available as an instance in the `Pointwise` locale. -/
+protected def hasDistribPointwiseNeg {A} [Ring A] [Algebra R A] : HasDistribNeg (Submodule R A) :=
+  toAddSubmonoid_injective.hasDistribNeg _ neg_toAddSubmonoid mul_toAddSubmonoid
 #align submodule.has_distrib_pointwise_neg Submodule.hasDistribPointwiseNeg
 
 scoped[Pointwise] attribute [instance] Submodule.hasDistribPointwiseNeg

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -173,7 +173,7 @@ theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid := by
   dsimp [HMul.hMul, Mul.mul]  --porting note: added `hMul`
-  rw [map₂, supᵢ_toAddSubmonoid]
+  rw [map₂, iSup_toAddSubmonoid]
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
 
@@ -261,9 +261,9 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
     map f.toLinearMap (M * N) = map f.toLinearMap M * map f.toLinearMap N :=
   calc
     map f.toLinearMap (M * N) = ⨆ i : M, (N.map (LinearMap.mul R A i)).map f.toLinearMap :=
-      map_supᵢ _ _
+      map_iSup _ _
     _ = map f.toLinearMap M * map f.toLinearMap N := by
-      apply congr_arg supₛ
+      apply congr_arg sSup
       ext S
       constructor <;> rintro ⟨y, hy⟩
       · use ⟨f y, mem_map.mpr ⟨y.1, y.2, rfl⟩⟩  -- porting note: added `⟨⟩`
@@ -364,13 +364,13 @@ theorem mul_eq_span_mul_set (s t : Submodule R A) : s * t = span R ((s : Set A)
   map₂_eq_span_image2 _ s t
 #align submodule.mul_eq_span_mul_set Submodule.mul_eq_span_mul_set
 
-theorem supᵢ_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
-  map₂_supᵢ_left _ s t
-#align submodule.supr_mul Submodule.supᵢ_mul
+theorem iSup_mul (s : ι → Submodule R A) (t : Submodule R A) : (⨆ i, s i) * t = ⨆ i, s i * t :=
+  map₂_iSup_left _ s t
+#align submodule.supr_mul Submodule.iSup_mul
 
-theorem mul_supᵢ (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
-  map₂_supᵢ_right _ t s
-#align submodule.mul_supr Submodule.mul_supᵢ
+theorem mul_iSup (t : Submodule R A) (s : ι → Submodule R A) : (t * ⨆ i, s i) = ⨆ i, t * s i :=
+  map₂_iSup_right _ t s
+#align submodule.mul_supr Submodule.mul_iSup
 
 theorem mem_span_mul_finite_of_mem_mul {P Q : Submodule R A} {x : A} (hx : x ∈ P * Q) :
     ∃ T T' : Finset A, (T : Set A) ⊆ P ∧ (T' : Set A) ⊆ Q ∧ x ∈ span R (T * T' : Set A) :=

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -131,8 +131,7 @@ protected theorem map_one {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
 
 @[simp]
 theorem map_op_one :
-    map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 :=
-  by
+    map (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R A) = 1 := by
   ext x
   induction x using MulOpposite.rec'
   simp
@@ -140,8 +139,7 @@ theorem map_op_one :
 
 @[simp]
 theorem comap_op_one :
-    comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 :=
-  by
+    comap (↑(opLinearEquiv R : A ≃ₗ[R] Aᵐᵒᵖ) : A →ₗ[R] Aᵐᵒᵖ) (1 : Submodule R Aᵐᵒᵖ) = 1 := by
   ext
   simp
 #align submodule.comap_op_one Submodule.comap_op_one
@@ -264,8 +262,7 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
   calc
     map f.toLinearMap (M * N) = ⨆ i : M, (N.map (LinearMap.mul R A i)).map f.toLinearMap :=
       map_supᵢ _ _
-    _ = map f.toLinearMap M * map f.toLinearMap N :=
-      by
+    _ = map f.toLinearMap M * map f.toLinearMap N := by
       apply congr_arg supₛ
       ext S
       constructor <;> rintro ⟨y, hy⟩
@@ -429,8 +426,7 @@ theorem pow_mem_pow {x : A} (hx : x ∈ M) (n : ℕ) : x ^ n ∈ M ^ n :=
   pow_subset_pow _ <| Set.pow_mem_pow hx _
 #align submodule.pow_mem_pow Submodule.pow_mem_pow
 
-theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.toAddSubmonoid ^ n :=
-  by
+theorem pow_toAddSubmonoid {n : ℕ} (h : n ≠ 0) : (M ^ n).toAddSubmonoid = M.toAddSubmonoid ^ n := by
   induction' n with n ih
   · exact (h rfl).elim
   · rw [pow_succ, pow_succ, mul_toAddSubmonoid]

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -175,9 +175,7 @@ theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid := by
   dsimp [HMul.hMul, Mul.mul]  --porting note: added `hMul`
-  simp_rw [← LinearMap.mulLeft_toAddMonoidHom R, LinearMap.mulLeft, ← map_toAddSubmonoid _ N,
-    map₂]
-  rw [supᵢ_toAddSubmonoid]
+  rw [map₂, supᵢ_toAddSubmonoid]
   rfl
 #align submodule.mul_to_add_submonoid Submodule.mul_toAddSubmonoid
 
@@ -387,13 +385,13 @@ variable {M N P}
 
 theorem mem_span_singleton_mul {x y : A} : x ∈ span R {y} * P ↔ ∃ z ∈ P, y * z = x := by
   --porting note: need both `*` and `Mul.mul`
-  simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map, exists_prop]
+  simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map]
   rfl
 #align submodule.mem_span_singleton_mul Submodule.mem_span_singleton_mul
 
 theorem mem_mul_span_singleton {x y : A} : x ∈ P * span R {y} ↔ ∃ z ∈ P, z * y = x := by
   --porting note: need both `*` and `Mul.mul`
-  simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map_flip, exists_prop]
+  simp_rw [(· * ·), Mul.mul, map₂_span_singleton_eq_map_flip]
   rfl
 #align submodule.mem_mul_span_singleton Submodule.mem_mul_span_singleton
 
@@ -641,13 +639,13 @@ instance moduleSet : Module (SetSemiring A) (Submodule R A) where
   smul s P := span R (SetSemiring.down s) * P
   smul_add _ _ _ := mul_add _ _ _
   add_smul s t P := by
-    simp_rw [HSMul.hSMul, SMul.smul, SetSemiring.down_add, span_union, sup_mul, add_eq_sup]
+    simp_rw [HSMul.hSMul, SetSemiring.down_add, span_union, sup_mul, add_eq_sup]
   mul_smul s t P := by
-    simp_rw [HSMul.hSMul, SMul.smul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
+    simp_rw [HSMul.hSMul, SetSemiring.down_mul, ← mul_assoc, span_mul_span]
   one_smul P := by
-    simp_rw [HSMul.hSMul, SMul.smul, SetSemiring.down_one, ←one_eq_span_one_set, one_mul]
+    simp_rw [HSMul.hSMul, SetSemiring.down_one, ←one_eq_span_one_set, one_mul]
   zero_smul P := by
-    simp_rw [HSMul.hSMul, SMul.smul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
+    simp_rw [HSMul.hSMul, SetSemiring.down_zero, span_empty, bot_mul, bot_eq_zero]
   smul_zero _ := mul_bot _
 #align submodule.module_set Submodule.moduleSet
 

Mathport doesn't understand this, and apparently nor do many of the humans fixing the errors it creates.

If your #align statement complains the def doesn't exist, don't change the #align; work out why it doesn't exist instead.

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -258,7 +258,7 @@ theorem sup_mul : (M ⊔ N) * P = M * P ⊔ N * P :=
 #align submodule.sup_mul Submodule.sup_mul
 
 theorem mul_subset_mul : (↑M : Set A) * (↑N : Set A) ⊆ (↑(M * N) : Set A) :=
-  image2_subset_map₂ (LinearMap.Algebra.lmul R A).toLinearMap M N
+  image2_subset_map₂ (Algebra.lmul R A).toLinearMap M N
 #align submodule.mul_subset_mul Submodule.mul_subset_mul
 
 protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A') :

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -281,7 +281,6 @@ protected theorem map_mul {A'} [Semiring A'] [Algebra R A'] (f : A →ₐ[R] A')
         rw [f.toLinearMap_apply] at fy_eq
         ext
         simp [fy_eq]
-
 #align submodule.map_mul Submodule.map_mul
 
 theorem map_op_mul :

@@ -175,7 +175,7 @@ theorem mul_le : M * N ≤ P ↔ ∀ m ∈ M, ∀ n ∈ N, m * n ∈ P :=
 theorem mul_toAddSubmonoid (M N : Submodule R A) :
     (M * N).toAddSubmonoid = M.toAddSubmonoid * N.toAddSubmonoid := by
   dsimp [HMul.hMul, Mul.mul]  --porting note: added `hMul`
-  simp_rw [← LinearMap.mulLeft_toAddMonoid_hom R, LinearMap.mulLeft, ← map_toAddSubmonoid _ N,
+  simp_rw [← LinearMap.mulLeft_toAddMonoidHom R, LinearMap.mulLeft, ← map_toAddSubmonoid _ N,
     map₂]
   rw [supᵢ_toAddSubmonoid]
   rfl

This had some trouble with leanprover/lean4#2074 and leanprover/lean4#1926. There are also quite a few places where extra unfolding is needed in initializers for new-style structures.

Co-authored-by: Johan Commelin <johan@commelin.net>